LMFDB - Embedded newform 64.2.i.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	64.29
Dual form			64.2.i.a.53.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40388 - 0.170631i) q^{2} +(-2.23702 - 0.444970i) q^{3} +(1.94177 + 0.479090i) q^{4} +(-2.33237 + 3.49064i) q^{5} +(3.06458 + 1.00639i) q^{6} +(-1.63661 + 0.677907i) q^{7} +(-2.64427 - 1.00391i) q^{8} +(2.03460 + 0.842759i) q^{9} +O(q^{10})$	\(q+(-1.40388 - 0.170631i) q^{2} +(-2.23702 - 0.444970i) q^{3} +(1.94177 + 0.479090i) q^{4} +(-2.33237 + 3.49064i) q^{5} +(3.06458 + 1.00639i) q^{6} +(-1.63661 + 0.677907i) q^{7} +(-2.64427 - 1.00391i) q^{8} +(2.03460 + 0.842759i) q^{9} +(3.86998 - 4.50247i) q^{10} +(-0.234463 - 1.17872i) q^{11} +(-4.13059 - 1.93576i) q^{12} +(-0.154344 - 0.230992i) q^{13} +(2.41328 - 0.672446i) q^{14} +(6.77078 - 6.77078i) q^{15} +(3.54094 + 1.86057i) q^{16} +(1.16542 + 1.16542i) q^{17} +(-2.71254 - 1.53030i) q^{18} +(-2.64509 + 1.76739i) q^{19} +(-6.20126 + 5.66061i) q^{20} +(3.96278 - 0.788246i) q^{21} +(0.128032 + 1.69479i) q^{22} +(-1.18934 + 2.87131i) q^{23} +(5.46856 + 3.42239i) q^{24} +(-4.83120 - 11.6635i) q^{25} +(0.177266 + 0.350621i) q^{26} +(1.51292 + 1.01090i) q^{27} +(-3.50271 + 0.532255i) q^{28} +(-0.141213 + 0.709928i) q^{29} +(-10.6607 + 8.35008i) q^{30} +7.01473i q^{31} +(-4.65360 - 3.21621i) q^{32} +2.74115i q^{33} +(-1.43726 - 1.83497i) q^{34} +(1.45086 - 7.29396i) q^{35} +(3.54697 + 2.61120i) q^{36} +(7.22008 + 4.82430i) q^{37} +(4.01496 - 2.02987i) q^{38} +(0.242485 + 0.585411i) q^{39} +(9.67171 - 6.88870i) q^{40} +(-0.152591 + 0.368387i) q^{41} +(-5.69777 + 0.430433i) q^{42} +(-4.98611 + 0.991798i) q^{43} +(0.109442 - 2.40114i) q^{44} +(-7.68722 + 5.13643i) q^{45} +(2.15962 - 3.82804i) q^{46} +(2.16092 + 2.16092i) q^{47} +(-7.09325 - 5.73773i) q^{48} +(-2.73080 + 2.73080i) q^{49} +(4.79227 + 17.1986i) q^{50} +(-2.08849 - 3.12564i) q^{51} +(-0.189034 - 0.522478i) q^{52} +(-1.84431 - 9.27195i) q^{53} +(-1.95147 - 1.67733i) q^{54} +(4.66135 + 1.93079i) q^{55} +(5.00821 - 0.149555i) q^{56} +(6.70353 - 2.77669i) q^{57} +(0.319382 - 0.972559i) q^{58} +(3.85360 - 5.76732i) q^{59} +(16.3911 - 9.90349i) q^{60} +(-9.69397 - 1.92825i) q^{61} +(1.19693 - 9.84785i) q^{62} -3.90117 q^{63} +(5.98432 + 5.30923i) q^{64} +1.16630 q^{65} +(0.467724 - 3.84825i) q^{66} +(7.14707 + 1.42164i) q^{67} +(1.70464 + 2.82132i) q^{68} +(3.93821 - 5.89395i) q^{69} +(-3.28141 + 9.99230i) q^{70} +(-4.28878 + 1.77647i) q^{71} +(-4.53398 - 4.27104i) q^{72} +(-3.39319 - 1.40550i) q^{73} +(-9.31297 - 8.00472i) q^{74} +(5.61753 + 28.2413i) q^{75} +(-5.98289 + 2.16463i) q^{76} +(1.18279 + 1.77017i) q^{77} +(-0.240532 - 0.863224i) q^{78} +(-1.54634 + 1.54634i) q^{79} +(-14.7534 + 8.02063i) q^{80} +(-7.60625 - 7.60625i) q^{81} +(0.277078 - 0.491135i) q^{82} +(-9.93110 + 6.63575i) q^{83} +(8.07245 + 0.367937i) q^{84} +(-6.78626 + 1.34987i) q^{85} +(7.16914 - 0.541586i) q^{86} +(0.631793 - 1.52528i) q^{87} +(-0.563352 + 3.35224i) q^{88} +(3.81437 + 9.20870i) q^{89} +(11.6684 - 5.89927i) q^{90} +(0.409193 + 0.273414i) q^{91} +(-3.68503 + 5.00563i) q^{92} +(3.12134 - 15.6921i) q^{93} +(-2.66496 - 3.40240i) q^{94} -13.3552i q^{95} +(8.97906 + 9.26542i) q^{96} +9.29602i q^{97} +(4.29968 - 3.36777i) q^{98} +(0.516342 - 2.59583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40388	−	0.170631i	−0.992695	−	0.120654i
$2$	−1.40388	−	0.170631i	−0.992695	−	0.120654i
$3$	−2.23702	−	0.444970i	−1.29154	−	0.256904i	−0.498936	−	0.866639i	$-0.666276\pi$
$3$	−2.23702	−	0.444970i	−1.29154	−	0.256904i	−0.792605	+	0.609735i	$0.791276\pi$
$4$	1.94177	+	0.479090i	0.970885	+	0.239545i
$5$	−2.33237	+	3.49064i	−1.04307	+	1.56106i	−0.234980	+	0.972000i	$0.575502\pi$
$5$	−2.33237	+	3.49064i	−1.04307	+	1.56106i	−0.808088	+	0.589061i	$0.799498\pi$
$6$	3.06458	+	1.00639i	1.25111	+	0.410856i
$7$	−1.63661	+	0.677907i	−0.618582	+	0.256225i	−0.669893	−	0.742458i	$-0.733660\pi$
$7$	−1.63661	+	0.677907i	−0.618582	+	0.256225i	0.0513111	+	0.998683i	$0.483660\pi$
$8$	−2.64427	−	1.00391i	−0.934890	−	0.354936i
$9$	2.03460	+	0.842759i	0.678200	+	0.280920i
$10$	3.86998	−	4.50247i	1.22380	−	1.42381i
$11$	−0.234463	−	1.17872i	−0.0706931	−	0.355398i	0.929207	−	0.369561i	$-0.120492\pi$
$11$	−0.234463	−	1.17872i	−0.0706931	−	0.355398i	−0.999900	+	0.0141624i	$0.995492\pi$
$12$	−4.13059	−	1.93576i	−1.19240	−	0.558806i
$13$	−0.154344	−	0.230992i	−0.0428073	−	0.0640657i	0.809449	−	0.587191i	$-0.199766\pi$
$13$	−0.154344	−	0.230992i	−0.0428073	−	0.0640657i	−0.852256	+	0.523125i	$0.824766\pi$
$14$	2.41328	−	0.672446i	0.644977	−	0.179719i
$15$	6.77078	−	6.77078i	1.74821	−	1.74821i
$16$	3.54094	+	1.86057i	0.885236	+	0.465142i
$17$	1.16542	+	1.16542i	0.282656	+	0.282656i	0.834167	−	0.551511i	$-0.185949\pi$
$17$	1.16542	+	1.16542i	0.282656	+	0.282656i	−0.551511	+	0.834167i	$0.685949\pi$
$18$	−2.71254	−	1.53030i	−0.639352	−	0.360695i
$19$	−2.64509	+	1.76739i	−0.606824	+	0.405467i	−0.820672	−	0.571400i	$-0.806400\pi$
$19$	−2.64509	+	1.76739i	−0.606824	+	0.405467i	0.213847	+	0.976867i	$0.431400\pi$
$20$	−6.20126	+	5.66061i	−1.38664	+	1.26575i
$21$	3.96278	−	0.788246i	0.864749	−	0.172009i
$22$	0.128032	+	1.69479i	0.0272964	+	0.361331i
$23$	−1.18934	+	2.87131i	−0.247994	+	0.598710i	−0.998033	−	0.0626831i	$-0.980034\pi$
$23$	−1.18934	+	2.87131i	−0.247994	+	0.598710i	0.750040	+	0.661393i	$0.230034\pi$
$24$	5.46856	+	3.42239i	1.11627	+	0.698592i
$25$	−4.83120	−	11.6635i	−0.966239	−	2.33271i
$26$	0.177266	+	0.350621i	0.0347648	+	0.0687625i
$27$	1.51292	+	1.01090i	0.291161	+	0.194548i
$28$	−3.50271	+	0.532255i	−0.661949	+	0.100587i
$29$	−0.141213	+	0.709928i	−0.0262227	+	0.131830i	−0.991679	−	0.128734i	$-0.958909\pi$
$29$	−0.141213	+	0.709928i	−0.0262227	+	0.131830i	0.965456	+	0.260564i	$0.0839086\pi$
$30$	−10.6607	+	8.35008i	−1.94637	+	1.52451i
$31$			7.01473i			1.25988i	0.776643	+	0.629941i	$0.216921\pi$
$31$			7.01473i			1.25988i	−0.776643	+	0.629941i	$0.783079\pi$
$32$	−4.65360	−	3.21621i	−0.822648	−	0.568551i
$33$			2.74115i			0.477173i
$34$	−1.43726	−	1.83497i	−0.246487	−	0.314695i
$35$	1.45086	−	7.29396i	0.245240	−	1.23290i
$36$	3.54697	+	2.61120i	0.591162	+	0.435201i
$37$	7.22008	+	4.82430i	1.18697	+	0.793111i	0.982591	−	0.185780i	$-0.0594813\pi$
$37$	7.22008	+	4.82430i	1.18697	+	0.793111i	0.204383	+	0.978891i	$0.434481\pi$
$38$	4.01496	−	2.02987i	0.651312	−	0.329289i
$39$	0.242485	+	0.585411i	0.0388287	+	0.0937408i
$40$	9.67171	−	6.88870i	1.52923	−	1.08920i
$41$	−0.152591	+	0.368387i	−0.0238307	+	0.0575323i	−0.935347	−	0.353732i	$-0.884913\pi$
$41$	−0.152591	+	0.368387i	−0.0238307	+	0.0575323i	0.911516	+	0.411264i	$0.134913\pi$
$42$	−5.69777	+	0.430433i	−0.879185	+	0.0664172i
$43$	−4.98611	+	0.991798i	−0.760374	+	0.151248i	−0.560024	−	0.828477i	$-0.689208\pi$
$43$	−4.98611	+	0.991798i	−0.760374	+	0.151248i	−0.200350	+	0.979724i	$0.564208\pi$
$44$	0.109442	−	2.40114i	0.0164990	−	0.361985i
$45$	−7.68722	+	5.13643i	−1.14594	+	0.765694i
$46$	2.15962	−	3.82804i	0.318419	−	0.564414i
$47$	2.16092	+	2.16092i	0.315203	+	0.315203i	0.846921	−	0.531719i	$-0.178454\pi$
$47$	2.16092	+	2.16092i	0.315203	+	0.315203i	−0.531719	+	0.846921i	$0.678454\pi$
$48$	−7.09325	−	5.73773i	−1.02382	−	0.828170i
$49$	−2.73080	+	2.73080i	−0.390115	+	0.390115i
$50$	4.79227	+	17.1986i	0.677730	+	2.43225i
$51$	−2.08849	−	3.12564i	−0.292447	−	0.437677i
$52$	−0.189034	−	0.522478i	−0.0262144	−	0.0724547i
$53$	−1.84431	−	9.27195i	−0.253335	−	1.27360i	−0.872607	−	0.488423i	$-0.837572\pi$
$53$	−1.84431	−	9.27195i	−0.253335	−	1.27360i	0.619272	−	0.785177i	$-0.287428\pi$
$54$	−1.95147	−	1.67733i	−0.265561	−	0.228256i
$55$	4.66135	+	1.93079i	0.628536	+	0.260348i
$56$	5.00821	−	0.149555i	0.669250	−	0.0199851i
$57$	6.70353	−	2.77669i	0.887905	−	0.367782i
$58$	0.319382	−	0.972559i	0.0419370	−	0.127703i
$59$	3.85360	−	5.76732i	0.501696	−	0.750840i	−0.491043	−	0.871136i	$-0.663384\pi$
$59$	3.85360	−	5.76732i	0.501696	−	0.750840i	0.992738	+	0.120295i	$0.0383841\pi$
$60$	16.3911	−	9.90349i	2.11608	−	1.27853i
$61$	−9.69397	−	1.92825i	−1.24119	−	0.246887i	−0.469524	−	0.882920i	$-0.655574\pi$
$61$	−9.69397	−	1.92825i	−1.24119	−	0.246887i	−0.771662	+	0.636033i	$0.780574\pi$
$62$	1.19693	−	9.84785i	0.152010	−	1.25068i
$63$	−3.90117			−0.491501
$64$	5.98432	+	5.30923i	0.748040	+	0.663653i
$65$	1.16630			0.144661
$66$	0.467724	−	3.84825i	0.0575728	−	0.473687i
$67$	7.14707	+	1.42164i	0.873153	+	0.173681i	0.611273	−	0.791420i	$-0.290658\pi$
$67$	7.14707	+	1.42164i	0.873153	+	0.173681i	0.261880	+	0.965100i	$0.415658\pi$
$68$	1.70464	+	2.82132i	0.206718	+	0.342135i
$69$	3.93821	−	5.89395i	0.474105	−	0.709548i
$70$	−3.28141	+	9.99230i	−0.392203	+	1.19431i
$71$	−4.28878	+	1.77647i	−0.508984	+	0.210828i	−0.622370	−	0.782723i	$-0.713830\pi$
$71$	−4.28878	+	1.77647i	−0.508984	+	0.210828i	0.113386	+	0.993551i	$0.463830\pi$
$72$	−4.53398	−	4.27104i	−0.534334	−	0.503347i
$73$	−3.39319	−	1.40550i	−0.397142	−	0.164502i	0.175169	−	0.984538i	$-0.443953\pi$
$73$	−3.39319	−	1.40550i	−0.397142	−	0.164502i	−0.572311	+	0.820037i	$0.693953\pi$
$74$	−9.31297	−	8.00472i	−1.08261	−	0.930530i
$75$	5.61753	+	28.2413i	0.648657	+	3.26102i
$76$	−5.98289	+	2.16463i	−0.686284	+	0.248300i
$77$	1.18279	+	1.77017i	0.134791	+	0.201730i
$78$	−0.240532	−	0.863224i	−0.0272349	−	0.0977408i
$79$	−1.54634	+	1.54634i	−0.173977	+	0.173977i	−0.788724	−	0.614747i	$-0.789258\pi$
$79$	−1.54634	+	1.54634i	−0.173977	+	0.173977i	0.614747	+	0.788724i	$0.289258\pi$
$80$	−14.7534	+	8.02063i	−1.64948	+	0.896734i
$81$	−7.60625	−	7.60625i	−0.845139	−	0.845139i
$82$	0.277078	−	0.491135i	0.0305981	−	0.0542368i
$83$	−9.93110	+	6.63575i	−1.09008	+	0.728368i	−0.964597	−	0.263728i	$-0.915048\pi$
$83$	−9.93110	+	6.63575i	−1.09008	+	0.728368i	−0.125483	+	0.992096i	$0.540048\pi$
$84$	8.07245	+	0.367937i	0.880776	+	0.0401452i
$85$	−6.78626	+	1.34987i	−0.736073	+	0.146414i
$86$	7.16914	−	0.541586i	0.773068	−	0.0584007i
$87$	0.631793	−	1.52528i	0.0677353	−	0.163528i
$88$	−0.563352	+	3.35224i	−0.0600535	+	0.357350i
$89$	3.81437	+	9.20870i	0.404322	+	0.976120i	0.986604	+	0.163133i	$0.0521600\pi$
$89$	3.81437	+	9.20870i	0.404322	+	0.976120i	−0.582282	+	0.812987i	$0.697840\pi$
$90$	11.6684	−	5.89927i	1.22995	−	0.621838i
$91$	0.409193	+	0.273414i	0.0428950	+	0.0286616i
$92$	−3.68503	+	5.00563i	−0.384191	+	0.521873i
$93$	3.12134	−	15.6921i	0.323668	−	1.62719i
$94$	−2.66496	−	3.40240i	−0.274869	−	0.350930i
$95$		−	13.3552i		−	1.37022i
$96$	8.97906	+	9.26542i	0.916421	+	0.945648i
$97$			9.29602i			0.943868i	0.881634	+	0.471934i	$0.156444\pi$
$97$			9.29602i			0.943868i	−0.881634	+	0.471934i	$0.843556\pi$
$98$	4.29968	−	3.36777i	0.434334	−	0.340196i
$99$	0.516342	−	2.59583i	0.0518943	−	0.260890i
$100$	−3.79318	−	24.9625i	−0.379318	−	2.49625i
$101$	6.78178	+	4.53144i	0.674813	+	0.450895i	0.845177	−	0.534486i	$-0.179495\pi$
$101$	6.78178	+	4.53144i	0.674813	+	0.450895i	−0.170365	+	0.985381i	$0.554495\pi$
$102$	2.39866	+	4.74439i	0.237503	+	0.469765i
$103$	−2.37519	−	5.73422i	−0.234035	−	0.565009i	0.762610	−	0.646858i	$-0.223917\pi$
$103$	−2.37519	−	5.73422i	−0.234035	−	0.565009i	−0.996645	+	0.0818489i	$0.973917\pi$
$104$	0.176231	+	0.765753i	0.0172809	+	0.0750882i
$105$	−6.49119	+	15.6711i	−0.633475	+	1.52934i
$106$	1.00711	+	13.3314i	0.0978191	+	1.29486i
$107$	18.1355	−	3.60738i	1.75323	−	0.348738i	0.789117	−	0.614243i	$-0.210539\pi$
$107$	18.1355	−	3.60738i	1.75323	−	0.348738i	0.964110	+	0.265504i	$0.0855385\pi$
$108$	2.45343	+	2.68776i	0.236081	+	0.258630i
$109$	−4.97622	+	3.32500i	−0.476636	+	0.318478i	−0.770578	−	0.637345i	$-0.780032\pi$
$109$	−4.97622	+	3.32500i	−0.476636	+	0.318478i	0.293943	+	0.955823i	$0.405032\pi$
$110$	−6.21453	−	3.50598i	−0.592533	−	0.334282i
$111$	−14.0048	−	14.0048i	−1.32927	−	1.32927i
$112$	−7.05645	−	0.644596i	−0.666772	−	0.0609086i
$113$	−2.54136	+	2.54136i	−0.239071	+	0.239071i	−0.816465	−	0.577394i	$-0.804070\pi$
$113$	−2.54136	+	2.54136i	−0.239071	+	0.239071i	0.577394	+	0.816465i	$0.304070\pi$
$114$	−9.88476	+	2.75432i	−0.925792	+	0.257966i
$115$	−7.24874	−	10.8485i	−0.675948	−	1.01163i
$116$	−0.614323	+	1.31086i	−0.0570385	+	0.121711i
$117$	−0.119358	−	0.600052i	−0.0110346	−	0.0554748i
$118$	−6.39408	+	7.43909i	−0.588622	+	0.684824i
$119$	−2.69739	−	1.11730i	−0.247269	−	0.102422i
$120$	−24.7010	+	11.1065i	−2.25489	+	1.01388i
$121$	8.82826	−	3.65679i	0.802569	−	0.332435i
$122$	13.2802	+	4.36113i	1.20233	+	0.394838i
$123$	0.505269	−	0.756189i	0.0455586	−	0.0681832i
$124$	−3.36069	+	13.6210i	−0.301799	+	1.22320i
$125$	31.3939	+	6.24464i	2.80796	+	0.558537i
$126$	5.47678	+	0.665659i	0.487910	+	0.0593016i
$127$	6.27367			0.556698			0.278349	−	0.960480i	$-0.410213\pi$
$127$	6.27367			0.556698			0.278349	+	0.960480i	$0.410213\pi$
$128$	−7.49537	−	8.47464i	−0.662503	−	0.749059i
$129$	11.5953			1.02091
$130$	−1.63734	−	0.199006i	−0.143605	−	0.0174540i
$131$	14.9538	+	2.97450i	1.30652	+	0.259883i	0.798778	−	0.601625i	$-0.205480\pi$
$131$	14.9538	+	2.97450i	1.30652	+	0.259883i	0.507743	+	0.861509i	$0.330480\pi$
$132$	−1.31326	+	5.32268i	−0.114304	+	0.463280i
$133$	3.13086	−	4.68566i	0.271480	−	0.406298i
$134$	−9.79106	−	3.21532i	−0.845819	−	0.277762i
$135$	−7.05737	+	2.92326i	−0.607402	+	0.251594i
$136$	−1.91171	−	4.25166i	−0.163927	−	0.364577i
$137$	3.38200	+	1.40087i	0.288944	+	0.119685i	0.522448	−	0.852671i	$-0.325019\pi$
$137$	3.38200	+	1.40087i	0.288944	+	0.119685i	−0.233504	+	0.972356i	$0.575019\pi$
$138$	−6.53447	+	7.60243i	−0.556251	+	0.647162i
$139$	−4.19783	−	21.1039i	−0.356055	−	1.79001i	−0.579158	−	0.815216i	$-0.696618\pi$
$139$	−4.19783	−	21.1039i	−0.356055	−	1.79001i	0.223102	−	0.974795i	$-0.428382\pi$
$140$	6.31170	−	13.4681i	0.533436	−	1.13826i
$141$	−3.87247	−	5.79555i	−0.326120	−	0.488074i
$142$	6.32406	−	1.76216i	0.530703	−	0.147877i
$143$	−0.236088	+	0.236088i	−0.0197426	+	0.0197426i
$144$	5.63640	+	6.76968i	0.469700	+	0.564140i
$145$	−2.14874	−	2.14874i	−0.178443	−	0.178443i
$146$	4.52381	+	2.55214i	0.374393	+	0.211217i
$147$	7.32397	−	4.89372i	0.604071	−	0.403627i
$148$	11.7085	+	12.8268i	0.962430	+	1.05435i
$149$	−8.61517	+	1.71366i	−0.705782	+	0.140389i	−0.534916	−	0.844905i	$-0.679657\pi$
$149$	−8.61517	+	1.71366i	−0.705782	+	0.140389i	−0.170867	+	0.985294i	$0.554657\pi$
$150$	−3.06754	−	40.6059i	−0.250463	−	3.31546i
$151$	−3.51806	+	8.49334i	−0.286295	+	0.691178i	−0.999957	−	0.00931286i	$-0.997036\pi$
$151$	−3.51806	+	8.49334i	−0.286295	+	0.691178i	0.713661	+	0.700491i	$0.247036\pi$
$152$	8.76862	−	2.01802i	0.711229	−	0.163683i
$153$	1.38900	+	3.35334i	0.112294	+	0.271101i
$154$	−1.35845	−	2.68693i	−0.109467	−	0.216519i
$155$	−24.4859	−	16.3610i	−1.96675	−	1.31414i
$156$	0.190386	+	1.25291i	0.0152431	+	0.100313i
$157$	−1.02494	+	5.15272i	−0.0817990	+	0.411232i	0.918091	+	0.396371i	$0.129731\pi$
$157$	−1.02494	+	5.15272i	−0.0817990	+	0.411232i	−0.999890	+	0.0148608i	$0.995269\pi$
$158$	2.43473	−	1.90703i	0.193697	−	0.151715i
$159$			21.5622i			1.70999i
$160$	22.0806	−	8.74265i	1.74562	−	0.691167i
$161$		−	5.50548i		−	0.433893i
$162$	9.38042	+	11.9761i	0.736996	+	0.940934i
$163$	−3.54698	+	17.8319i	−0.277821	+	1.39670i	0.549745	+	0.835333i	$0.314725\pi$
$163$	−3.54698	+	17.8319i	−0.277821	+	1.39670i	−0.827566	+	0.561368i	$0.810275\pi$
$164$	−0.472787	+	0.642218i	−0.0369184	+	0.0501488i
$165$	−9.56837	−	6.39338i	−0.744896	−	0.497724i
$166$	15.0744	−	7.62126i	1.17000	−	0.591525i
$167$	−7.42288	−	17.9204i	−0.574400	−	1.38672i	−0.897776	−	0.440453i	$-0.854818\pi$
$167$	−7.42288	−	17.9204i	−0.574400	−	1.38672i	0.323376	−	0.946270i	$-0.395182\pi$
$168$	−11.2700	−	1.89395i	−0.869498	−	0.146121i
$169$	4.94535	−	11.9391i	0.380411	−	0.918395i
$170$	9.75743	−	0.737116i	0.748361	−	0.0565342i
$171$	−6.87118	+	1.36676i	−0.525452	+	0.104519i
$172$	−10.1570	−	0.462951i	−0.774466	−	0.0352997i
$173$	4.21489	−	2.81630i	0.320452	−	0.214119i	−0.384931	−	0.922945i	$-0.625775\pi$
$173$	4.21489	−	2.81630i	0.320452	−	0.214119i	0.705383	+	0.708826i	$0.250775\pi$
$174$	−1.14722	+	2.03352i	−0.0869708	+	0.154160i
$175$	15.8136	+	15.8136i	1.19540	+	1.19540i
$176$	1.36287	−	4.61003i	0.102730	−	0.347494i
$177$	−11.1868	+	11.1868i	−0.840854	+	0.840854i
$178$	−3.78364	−	13.5788i	−0.283596	−	1.01777i
$179$	9.57074	+	14.3236i	0.715351	+	1.07060i	0.993912	+	0.110180i	$0.0351426\pi$
$179$	9.57074	+	14.3236i	0.715351	+	1.07060i	−0.278561	+	0.960419i	$0.589857\pi$
$180$	−17.3876	+	6.29090i	−1.29600	+	0.468896i
$181$	2.13516	+	10.7342i	0.158705	+	0.797865i	0.975340	+	0.220710i	$0.0708374\pi$
$181$	2.13516	+	10.7342i	0.158705	+	0.797865i	−0.816634	+	0.577156i	$0.804163\pi$
$182$	−0.527805	−	0.453661i	−0.0391235	−	0.0336276i
$183$	20.8276	+	8.62705i	1.53962	+	0.637730i
$184$	6.02747	−	6.39853i	0.444351	−	0.471706i
$185$	−33.6798	+	13.9506i	−2.47619	+	1.02567i
$186$	−7.05954	+	21.4972i	−0.517631	+	1.57625i
$187$	1.10046	−	1.64696i	0.0804736	−	0.120437i
$188$	3.16073	+	5.23129i	0.230520	+	0.381531i
$189$	−3.16136	−	0.628833i	−0.229955	−	0.0457409i
$190$	−2.27881	+	18.7492i	−0.165323	+	1.36021i
$191$	−20.6704			−1.49566			−0.747830	−	0.663890i	$-0.768904\pi$
$191$	−20.6704			−1.49566			−0.747830	+	0.663890i	$0.768904\pi$
$192$	−11.0246	−	14.5397i	−0.795630	−	1.04931i
$193$	19.6483			1.41432			0.707158	−	0.707056i	$-0.249977\pi$
$193$	19.6483			1.41432			0.707158	+	0.707056i	$0.249977\pi$
$194$	1.58619	−	13.0505i	0.113881	−	0.936973i
$195$	−2.60903	−	0.518967i	−0.186836	−	0.0371640i
$196$	−6.61089	+	3.99429i	−0.472207	+	0.285306i
$197$	−11.3923	+	17.0498i	−0.811669	+	1.21475i	0.162001	+	0.986791i	$0.448205\pi$
$197$	−11.3923	+	17.0498i	−0.811669	+	1.21475i	−0.973671	+	0.227959i	$0.926795\pi$
$198$	−1.16781	+	3.55613i	−0.0829927	+	0.252723i
$199$	1.25587	−	0.520198i	0.0890262	−	0.0368759i	−0.337726	−	0.941245i	$-0.609658\pi$
$199$	1.25587	−	0.520198i	0.0890262	−	0.0368759i	0.426752	+	0.904369i	$0.359658\pi$
$200$	1.06582	+	35.6916i	0.0753649	+	2.52378i
$201$	−15.3555	−	6.36046i	−1.08309	−	0.448632i
$202$	−8.74762	−	7.51879i	−0.615480	−	0.529020i
$203$	−0.250154	−	1.25761i	−0.0175573	−	0.0882667i
$204$	−2.55790	−	7.06985i	−0.179089	−	0.494989i
$205$	−0.930007	−	1.39185i	−0.0649545	−	0.0972113i
$206$	2.35606	+	8.45545i	0.164154	+	0.589119i
$207$	−4.83965	+	4.83965i	−0.336379	+	0.336379i
$208$	−0.116747	−	1.10510i	−0.00809497	−	0.0766247i
$209$	2.70344	+	2.70344i	0.187001	+	0.187001i
$210$	11.7868	−	20.8928i	0.813369	−	1.44174i
$211$	9.24556	−	6.17768i	0.636490	−	0.425289i	−0.195019	−	0.980799i	$-0.562477\pi$
$211$	9.24556	−	6.17768i	0.636490	−	0.425289i	0.831510	+	0.555510i	$0.187477\pi$
$212$	0.860884	−	18.8876i	0.0591257	−	1.29720i
$213$	10.3845	−	2.06561i	0.711537	−	0.141533i
$214$	−26.0757	+	1.96986i	−1.78250	+	0.134657i
$215$	8.16744	−	19.7179i	0.557015	−	1.34475i
$216$	−2.98571	−	4.19193i	−0.203152	−	0.285225i
$217$	−4.75534	−	11.4804i	−0.322813	−	0.779340i
$218$	7.55338	−	3.81882i	0.511579	−	0.258643i
$219$	6.96520	+	4.65400i	0.470665	+	0.314488i
$220$	8.12625	+	5.98237i	0.547872	+	0.403331i
$221$	0.0893273	−	0.449078i	0.00600880	−	0.0302083i
$222$	17.2714	+	22.0507i	1.15918	+	1.47994i
$223$			0.398929i			0.0267143i	0.999911	+	0.0133571i	$0.00425183\pi$
$223$			0.398929i			0.0267143i	−0.999911	+	0.0133571i	$0.995748\pi$
$224$	9.79644	+	2.10898i	0.654552	+	0.140912i
$225$		−	27.8022i		−	1.85348i
$226$	4.00140	−	3.13414i	0.266169	−	0.208480i
$227$	−2.31877	+	11.6572i	−0.153902	+	0.773718i	0.824315	+	0.566132i	$0.191561\pi$
$227$	−2.31877	+	11.6572i	−0.153902	+	0.773718i	−0.978217	+	0.207586i	$0.933439\pi$
$228$	14.3470	−	2.18010i	0.950154	−	0.144381i
$229$	−5.87305	−	3.92425i	−0.388102	−	0.259322i	0.346177	−	0.938169i	$-0.387480\pi$
$229$	−5.87305	−	3.92425i	−0.388102	−	0.259322i	−0.734279	+	0.678848i	$0.762480\pi$
$230$	8.32529	+	16.4669i	0.548953	+	1.08579i
$231$	−1.85825	−	4.48620i	−0.122264	−	0.295170i
$232$	1.08611	−	1.73547i	0.0713067	−	0.113939i
$233$	−2.63067	+	6.35099i	−0.172341	+	0.416067i	−0.986323	−	0.164822i	$-0.947295\pi$
$233$	−2.63067	+	6.35099i	−0.172341	+	0.416067i	0.813983	+	0.580889i	$0.197295\pi$
$234$	0.0651770	+	0.862768i	0.00426075	+	0.0564009i
$235$	−12.5831	+	2.50293i	−0.820828	+	0.163273i
$236$	10.2459	−	9.35258i	0.666949	−	0.608801i
$237$	4.14727	−	2.77111i	0.269394	−	0.180003i
$238$	3.59617	+	2.02881i	0.233105	+	0.131508i
$239$	2.18529	+	2.18529i	0.141355	+	0.141355i	0.774243	−	0.632888i	$-0.218131\pi$
$239$	2.18529	+	2.18529i	0.141355	+	0.141355i	−0.632888	+	0.774243i	$0.718131\pi$
$240$	36.5725	−	11.3775i	2.36074	−	0.734413i
$241$	9.11533	−	9.11533i	0.587170	−	0.587170i	−0.349694	−	0.936864i	$-0.613714\pi$
$241$	9.11533	−	9.11533i	0.587170	−	0.587170i	0.936864	+	0.349694i	$0.113714\pi$
$242$	−13.0178	+	3.62732i	−0.836816	+	0.233173i
$243$	10.5980	+	15.8611i	0.679865	+	1.01749i
$244$	−17.8997	−	8.38851i	−1.14591	−	0.537019i
$245$	−3.16300	−	15.9015i	−0.202077	−	1.01591i
$246$	−0.838367	+	0.975385i	−0.0534523	+	0.0621883i
$247$	0.816506	+	0.338208i	0.0519530	+	0.0215196i
$248$	7.04217	−	18.5488i	0.447178	−	1.17785i
$249$	25.1687	−	10.4252i	1.59500	−	0.660672i
$250$	−43.0078	−	14.1235i	−2.72005	−	0.893248i
$251$	−10.9216	+	16.3453i	−0.689364	+	1.03171i	0.307420	+	0.951574i	$0.400534\pi$
$251$	−10.9216	+	16.3453i	−0.689364	+	1.03171i	−0.996784	+	0.0801321i	$0.974466\pi$
$252$	−7.57517	−	1.86901i	−0.477191	−	0.117737i
$253$	3.66333	+	0.728682i	0.230312	+	0.0458119i
$254$	−8.80749	−	1.07048i	−0.552631	−	0.0671679i
$255$	15.7816			0.988283
$256$	9.07658	+	13.1763i	0.567286	+	0.823521i
$257$	−16.2065			−1.01093			−0.505466	−	0.862846i	$-0.668680\pi$
$257$	−16.2065			−1.01093			−0.505466	+	0.862846i	$0.668680\pi$
$258$	−16.2785	−	1.97851i	−1.01345	−	0.123177i
$259$	−15.0869	−	3.00097i	−0.937455	−	0.186471i
$260$	2.26468	+	0.558762i	0.140450	+	0.0346529i
$261$	−0.885611	+	1.32541i	−0.0548180	+	0.0820409i
$262$	−20.4859	−	6.72743i	−1.26562	−	0.415622i
$263$	22.6730	−	9.39145i	1.39808	−	0.579102i	0.448824	−	0.893620i	$-0.351843\pi$
$263$	22.6730	−	9.39145i	1.39808	−	0.579102i	0.949251	+	0.314518i	$0.101843\pi$
$264$	2.75187	−	7.24834i	0.169366	−	0.446104i
$265$	36.6666	+	15.1878i	2.25241	+	0.932980i
$266$	−5.19487	+	6.04389i	−0.318518	+	0.370575i
$267$	−4.43521	−	22.2973i	−0.271430	−	1.36457i
$268$	13.1969	+	6.18459i	0.806127	+	0.377784i
$269$	0.381447	+	0.570875i	0.0232572	+	0.0348069i	0.842916	−	0.538045i	$-0.180837\pi$
$269$	0.381447	+	0.570875i	0.0232572	+	0.0348069i	−0.819659	+	0.572852i	$0.805837\pi$
$270$	10.4065	−	2.89971i	0.633321	−	0.176471i
$271$	10.0189	−	10.0189i	0.608606	−	0.608606i	−0.333975	−	0.942582i	$-0.608390\pi$
$271$	10.0189	−	10.0189i	0.608606	−	0.608606i	0.942582	+	0.333975i	$0.108390\pi$
$272$	1.95835	+	6.29503i	0.118742	+	0.381692i
$273$	−0.793709	−	0.793709i	−0.0480375	−	0.0480375i
$274$	−4.50890	−	2.54373i	−0.272393	−	0.153672i
$275$	−12.6153	+	8.42930i	−0.760734	+	0.508306i
$276$	10.4708	−	9.55793i	0.630270	−	0.575320i
$277$	−22.7599	+	4.52722i	−1.36751	+	0.272014i	−0.823619	−	0.567143i	$-0.808049\pi$
$277$	−22.7599	+	4.52722i	−1.36751	+	0.272014i	−0.543889	+	0.839157i	$0.683049\pi$
$278$	2.29229	+	30.3437i	0.137482	+	1.81989i
$279$	−5.91173	+	14.2722i	−0.353926	+	0.854453i
$280$	−11.1590	+	17.8307i	−0.666875	+	1.06559i
$281$	1.29852	+	3.13490i	0.0774631	+	0.187012i	0.957867	−	0.287212i	$-0.0927285\pi$
$281$	1.29852	+	3.13490i	0.0774631	+	0.187012i	−0.880404	+	0.474225i	$0.842728\pi$
$282$	4.44759	+	8.79704i	0.264850	+	0.523856i
$283$	10.2454	+	6.84576i	0.609026	+	0.406938i	0.821484	−	0.570232i	$-0.193147\pi$
$283$	10.2454	+	6.84576i	0.609026	+	0.406938i	−0.212458	+	0.977170i	$0.568147\pi$
$284$	−9.17891	+	1.39478i	−0.544668	+	0.0827652i
$285$	−5.94269	+	29.8759i	−0.352014	+	1.76970i
$286$	0.371723	−	0.291156i	0.0219804	−	0.0172164i
$287$		−	0.706349i		−	0.0416945i
$288$	−6.75773	−	10.4656i	−0.398203	−	0.616690i
$289$		−	14.2836i		−	0.840211i
$290$	2.64994	+	3.38322i	0.155610	+	0.198669i
$291$	4.13645	−	20.7953i	0.242483	−	1.21904i
$292$	−5.91543	−	4.35481i	−0.346174	−	0.254846i
$293$	−11.3488	−	7.58301i	−0.663003	−	0.443004i	0.178004	−	0.984030i	$-0.443036\pi$
$293$	−11.3488	−	7.58301i	−0.663003	−	0.443004i	−0.841006	+	0.541026i	$0.818036\pi$
$294$	−11.1170	+	5.62052i	−0.648357	+	0.327795i
$295$	11.1436	+	26.9030i	0.648806	+	1.56636i
$296$	−14.2487	−	20.0051i	−0.828187	−	1.16277i
$297$	0.836848	−	2.02033i	0.0485588	−	0.117231i
$298$	12.3871	−	0.935771i	0.717565	−	0.0542078i
$299$	0.846817	−	0.168442i	0.0489727	−	0.00974127i
$300$	−2.62215	+	57.5293i	−0.151390	+	3.32146i
$301$	7.48798	−	5.00331i	0.431600	−	0.288386i
$302$	6.38816	−	11.3234i	0.367597	−	0.651586i
$303$	−13.1546	−	13.1546i	−0.755712	−	0.755712i
$304$	−12.6544	+	1.33687i	−0.725782	+	0.0766748i
$305$	29.3408	−	29.3408i	1.68005	−	1.68005i
$306$	−1.37781	−	4.94469i	−0.0787640	−	0.282669i
$307$	−14.2506	−	21.3276i	−0.813326	−	1.21723i	−0.973170	−	0.230086i	$-0.926099\pi$
$307$	−14.2506	−	21.3276i	−0.813326	−	1.21723i	0.159844	−	0.987142i	$-0.448901\pi$
$308$	1.44863	+	4.00393i	0.0825436	+	0.228145i
$309$	2.76178	+	13.8844i	0.157112	+	0.789857i
$310$	31.5836	+	27.1469i	1.79383	+	1.54184i
$311$	8.17983	+	3.38820i	0.463835	+	0.192127i	0.602348	−	0.798234i	$-0.294232\pi$
$311$	8.17983	+	3.38820i	0.463835	+	0.192127i	−0.138512	+	0.990361i	$0.544232\pi$
$312$	−0.0534952	−	1.79142i	−0.00302857	−	0.101419i
$313$	−3.15454	+	1.30665i	−0.178305	+	0.0738564i	−0.470050	−	0.882640i	$-0.655764\pi$
$313$	−3.15454	+	1.30665i	−0.178305	+	0.0738564i	0.291745	+	0.956496i	$0.405764\pi$
$314$	2.31810	−	7.05892i	0.130818	−	0.398358i
$315$	9.09897	−	13.6176i	0.512669	−	0.767264i
$316$	−3.74348	+	2.26180i	−0.210587	+	0.127236i
$317$	−17.1528	−	3.41191i	−0.963399	−	0.191632i	−0.311760	−	0.950161i	$-0.600918\pi$
$317$	−17.1528	−	3.41191i	−0.963399	−	0.191632i	−0.651639	+	0.758529i	$0.725918\pi$
$318$	3.67916	−	30.2707i	0.206317	−	1.69750i
$319$	0.869917			0.0487060
$320$	−32.4903	+	8.50603i	−1.81626	+	0.475501i
$321$	−42.1746			−2.35396
$322$	−0.939404	+	7.72905i	−0.0523509	+	0.430723i
$323$	−5.14239	−	1.02288i	−0.286130	−	0.0569148i
$324$	−11.1255	−	18.4137i	−0.618084	−	1.02298i
$325$	−1.94852	+	2.91616i	−0.108084	+	0.161760i
$326$	8.02221	−	24.4286i	0.444309	−	1.35298i
$327$	12.6114	−	5.22382i	0.697413	−	0.288878i
$328$	0.773319	−	0.820926i	0.0426994	−	0.0453281i
$329$	−5.00149	−	2.07169i	−0.275741	−	0.114216i
$330$	12.3420	+	10.6082i	0.679402	+	0.583963i
$331$	2.90638	+	14.6113i	0.159749	+	0.803112i	0.974689	+	0.223566i	$0.0717699\pi$
$331$	2.90638	+	14.6113i	0.159749	+	0.803112i	−0.814940	+	0.579546i	$0.803230\pi$
$332$	−22.4630	+	8.12721i	−1.23282	+	0.446038i
$333$	10.6243	+	15.9003i	0.582206	+	0.871332i
$334$	7.36308	+	26.4247i	0.402890	+	1.44590i
$335$	−21.6320	+	21.6320i	−1.18188	+	1.18188i
$336$	15.4986	+	4.58188i	0.845516	+	0.249962i
$337$	−4.78263	−	4.78263i	−0.260527	−	0.260527i	0.564741	−	0.825268i	$-0.308976\pi$
$337$	−4.78263	−	4.78263i	−0.260527	−	0.260527i	−0.825268	+	0.564741i	$0.808976\pi$
$338$	−8.97987	+	15.9173i	−0.488440	+	0.865787i
$339$	6.81589	−	4.55423i	0.370188	−	0.247352i
$340$	−13.8241	−	0.630092i	−0.749715	−	0.0341715i
$341$	8.26842	−	1.64469i	0.447760	−	0.0890650i
$342$	9.87954	−	0.746341i	0.534224	−	0.0403575i
$343$	7.36339	−	17.7768i	0.397586	−	0.959857i
$344$	14.1803	+	2.38303i	0.764550	+	0.128484i
$345$	11.3883	+	27.4937i	0.613124	+	1.48021i
$346$	−6.39776	+	3.23457i	−0.343946	+	0.173891i
$347$	9.14973	+	6.11366i	0.491183	+	0.328198i	0.776374	−	0.630273i	$-0.217057\pi$
$347$	9.14973	+	6.11366i	0.491183	+	0.328198i	−0.285191	+	0.958471i	$0.592057\pi$
$348$	1.95755	−	2.65906i	0.104935	−	0.142541i
$349$	3.87593	−	19.4856i	0.207474	−	1.04304i	−0.726899	−	0.686744i	$-0.759039\pi$
$349$	3.87593	−	19.4856i	0.207474	−	1.04304i	0.934373	−	0.356297i	$-0.115961\pi$
$350$	−19.5021	−	24.8987i	−1.04243	−	1.33089i
$351$		−	0.505498i		−	0.0269815i
$352$	−2.69993	+	6.23939i	−0.143907	+	0.332560i
$353$			22.7162i			1.20906i	0.796583	+	0.604529i	$0.206639\pi$
$353$			22.7162i			1.20906i	−0.796583	+	0.604529i	$0.793361\pi$
$354$	17.6138	−	13.7962i	0.936164	−	0.733259i
$355$	3.80200	−	19.1140i	0.201789	−	1.01446i
$356$	2.99483	+	19.7086i	0.158726	+	1.04455i
$357$	5.53694	+	3.69967i	0.293046	+	0.195807i
$358$	−10.9921	−	21.7417i	−0.580953	−	1.14909i
$359$	14.0062	+	33.8139i	0.739218	+	1.78463i	0.609039	+	0.793140i	$0.291555\pi$
$359$	14.0062	+	33.8139i	0.739218	+	1.78463i	0.130179	+	0.991490i	$0.458445\pi$
$360$	25.4836	−	5.86483i	1.34310	−	0.309104i
$361$	−3.39817	+	8.20392i	−0.178851	+	0.431785i
$362$	−1.16594	−	15.4338i	−0.0612802	−	0.811185i
$363$	−21.3761	+	4.25197i	−1.12196	+	0.223171i
$364$	0.663568	+	0.726947i	0.0347804	+	0.0381024i
$365$	12.8203	−	8.56624i	0.671044	−	0.448377i
$366$	−27.7674	−	15.6652i	−1.45142	−	0.818832i
$367$	10.6394	+	10.6394i	0.555373	+	0.555373i	0.927987	−	0.372614i	$-0.121538\pi$
$367$	10.6394	+	10.6394i	0.555373	+	0.555373i	−0.372614	+	0.927987i	$0.621538\pi$
$368$	−9.55364	+	7.95431i	−0.498018	+	0.414647i
$369$	−0.620923	+	0.620923i	−0.0323240	+	0.0323240i
$370$	49.6629	−	13.8382i	2.58185	−	0.719416i
$371$	9.30394	+	13.9243i	0.483036	+	0.722915i
$372$	13.5788	−	28.9750i	0.704030	−	1.50228i
$373$	0.946981	+	4.76079i	0.0490328	+	0.246505i	0.997526	−	0.0702914i	$-0.0223929\pi$
$373$	0.946981	+	4.76079i	0.0490328	+	0.246505i	−0.948494	+	0.316796i	$0.897393\pi$
$374$	−1.82594	+	2.12436i	−0.0944170	+	0.109848i
$375$	−67.4500	−	27.9387i	−3.48310	−	1.44275i
$376$	−3.54468	−	7.88343i	−0.182803	−	0.406557i
$377$	0.185783	−	0.0769539i	0.00956831	−	0.00396333i
$378$	4.33088	+	1.42223i	0.222756	+	0.0731517i
$379$	−4.29469	+	6.42746i	−0.220603	+	0.330156i	−0.925219	−	0.379432i	$-0.876119\pi$
$379$	−4.29469	+	6.42746i	−0.220603	+	0.330156i	0.704616	+	0.709589i	$0.251119\pi$
$380$	6.39837	−	25.9328i	0.328230	−	1.33033i
$381$	−14.0343	−	2.79160i	−0.718999	−	0.143018i
$382$	29.0189	+	3.52701i	1.48473	+	0.180457i
$383$	−13.2624			−0.677675			−0.338837	−	0.940845i	$-0.610034\pi$
$383$	−13.2624			−0.677675			−0.338837	+	0.940845i	$0.610034\pi$
$384$	12.9963	+	22.2931i	0.663214	+	1.13764i
$385$	−8.93773			−0.455509
$386$	−27.5839	−	3.35260i	−1.40398	−	0.170643i
$387$	−10.9806	−	2.18417i	−0.558174	−	0.111028i
$388$	−4.45363	+	18.0507i	−0.226099	+	0.916387i
$389$	7.11261	−	10.6448i	0.360624	−	0.539711i	−0.606148	−	0.795352i	$-0.707286\pi$
$389$	7.11261	−	10.6448i	0.360624	−	0.539711i	0.966772	+	0.255640i	$0.0822863\pi$
$390$	3.57421	+	1.17375i	0.180987	+	0.0594351i
$391$	−4.73236	+	1.96021i	−0.239326	+	0.0991320i
$392$	9.96246	−	4.47949i	0.503180	−	0.226249i
$393$	−32.1284	−	13.3080i	−1.62066	−	0.671300i
$394$	18.9027	−	21.9921i	0.952304	−	1.10794i
$395$	−1.79108	−	9.00437i	−0.0901190	−	0.453059i
$396$	2.24625	−	4.79312i	0.112878	−	0.240864i
$397$	21.7727	+	32.5851i	1.09274	+	1.63540i	0.697064	+	0.717009i	$0.254489\pi$
$397$	21.7727	+	32.5851i	1.09274	+	1.63540i	0.395675	+	0.918390i	$0.370511\pi$
$398$	−1.85185	+	0.516007i	−0.0928251	+	0.0258651i
$399$	−9.08875	+	9.08875i	−0.455007	+	0.455007i
$400$	4.59380	−	50.2887i	0.229690	−	2.51444i
$401$	1.79901	+	1.79901i	0.0898380	+	0.0898380i	0.750598	−	0.660760i	$-0.229766\pi$
$401$	1.79901	+	1.79901i	0.0898380	+	0.0898380i	−0.660760	+	0.750598i	$0.729766\pi$
$402$	20.4720	+	11.5495i	1.02105	+	0.576035i
$403$	1.62035	−	1.08268i	0.0807152	−	0.0539322i
$404$	10.9977	+	12.0481i	0.547156	+	0.599416i
$405$	44.2913	−	8.81008i	2.20085	−	0.437777i
$406$	0.136600	+	1.80822i	0.00677934	+	0.0897402i
$407$	3.99368	−	9.64159i	0.197959	−	0.477916i
$408$	2.38465	+	10.3617i	0.118058	+	0.512980i
$409$	−2.64478	−	6.38506i	−0.130776	−	0.315721i	0.844905	−	0.534916i	$-0.179657\pi$
$409$	−2.64478	−	6.38506i	−0.130776	−	0.315721i	−0.975681	+	0.219195i	$0.929657\pi$
$410$	1.06813	+	2.11269i	0.0527511	+	0.104338i
$411$	−6.94225	−	4.63866i	−0.342436	−	0.228808i
$412$	−1.86487	−	12.2725i	−0.0918754	−	0.604621i
$413$	−2.39714	+	12.0512i	−0.117956	+	0.593003i
$414$	7.62009	−	5.96850i	0.374507	−	0.293336i
$415$		−	50.1429i		−	2.46142i
$416$	−0.0246640	+	1.57135i	−0.00120925	+	0.0770416i
$417$			49.0777i			2.40334i
$418$	−3.33402	−	4.25659i	−0.163072	−	0.208197i
$419$	−1.12208	+	5.64109i	−0.0548173	+	0.275585i	−0.998466	−	0.0553627i	$-0.982368\pi$
$419$	−1.12208	+	5.64109i	−0.0548173	+	0.275585i	0.943649	+	0.330948i	$0.107368\pi$
$420$	−20.1123	+	27.3198i	−0.981379	+	1.33307i
$421$	21.9884	+	14.6922i	1.07165	+	0.716052i	0.960648	−	0.277769i	$-0.0895949\pi$
$421$	21.9884	+	14.6922i	1.07165	+	0.716052i	0.110999	+	0.993821i	$0.464595\pi$
$422$	−14.0338	+	7.09517i	−0.683153	+	0.345387i
$423$	2.57547	+	6.21774i	0.125224	+	0.302317i
$424$	−4.43138	+	26.3690i	−0.215207	+	1.28059i
$425$	7.96255	−	19.2233i	0.386241	−	0.932467i
$426$	−14.9311	+	1.12796i	−0.723415	+	0.0546497i
$427$	17.1725	−	3.41581i	0.831034	−	0.165303i
$428$	36.9433	+	1.68385i	1.78572	+	0.0813920i
$429$	0.633184	−	0.423080i	0.0305704	−	0.0204265i
$430$	−14.8306	+	26.2881i	−0.715195	+	1.26772i
$431$	−5.66697	−	5.66697i	−0.272968	−	0.272968i	0.557326	−	0.830294i	$-0.311828\pi$
$431$	−5.66697	−	5.66697i	−0.272968	−	0.272968i	−0.830294	+	0.557326i	$0.811828\pi$
$432$	3.47631	+	6.39443i	0.167254	+	0.307652i
$433$	−9.43057	+	9.43057i	−0.453204	+	0.453204i	−0.896417	−	0.443212i	$-0.853839\pi$
$433$	−9.43057	+	9.43057i	−0.453204	+	0.453204i	0.443212	+	0.896417i	$0.353839\pi$
$434$	4.71703	+	16.9285i	0.226425	+	0.812596i
$435$	3.85064	+	5.76289i	0.184624	+	0.276309i
$436$	−11.2557	+	4.07234i	−0.539048	+	0.195030i
$437$	−1.92883	−	9.69688i	−0.0922684	−	0.463865i
$438$	−8.98421	−	7.72214i	−0.429282	−	0.368978i
$439$	−19.0108	−	7.87451i	−0.907334	−	0.375830i	−0.120299	−	0.992738i	$-0.538385\pi$
$439$	−19.0108	−	7.87451i	−0.907334	−	0.375830i	−0.787036	+	0.616908i	$0.788385\pi$
$440$	−10.3875	−	9.78513i	−0.495206	−	0.466488i
$441$	−7.85750	+	3.25468i	−0.374167	+	0.154985i
$442$	−0.202031	+	0.615211i	−0.00960966	+	0.0292626i
$443$	9.86124	−	14.7584i	0.468522	−	0.701193i	−0.519678	−	0.854362i	$-0.673948\pi$
$443$	9.86124	−	14.7584i	0.468522	−	0.701193i	0.988200	+	0.153170i	$0.0489481\pi$
$444$	−20.4845	−	33.9036i	−0.972151	−	1.60899i
$445$	−41.0408	−	8.16352i	−1.94552	−	0.386988i
$446$	0.0680695	−	0.560049i	0.00322318	−	0.0265191i
$447$	20.0348			0.947614
$448$	−13.3932	−	4.63233i	−0.632769	−	0.218857i
$449$	12.8596			0.606883			0.303441	−	0.952850i	$-0.401864\pi$
$449$	12.8596			0.606883			0.303441	+	0.952850i	$0.401864\pi$
$450$	−4.74390	+	39.0310i	−0.223630	+	1.83994i
$451$	0.470003	+	0.0934893i	0.0221316	+	0.00440224i
$452$	−6.15228	+	3.71720i	−0.289379	+	0.174842i
$453$	11.6492	−	17.4343i	0.547328	−	0.819135i
$454$	5.24436	−	15.9697i	0.246130	−	0.749497i
$455$	−1.90878	+	0.790642i	−0.0894849	+	0.0370659i
$456$	−20.5135	+	0.612572i	−0.960633	+	0.0286863i
$457$	4.61582	+	1.91193i	0.215919	+	0.0894365i	0.488021	−	0.872832i	$-0.337719\pi$
$457$	4.61582	+	1.91193i	0.215919	+	0.0894365i	−0.272102	+	0.962268i	$0.587719\pi$
$458$	7.57548	+	6.51131i	0.353979	+	0.304253i
$459$	0.585063	+	2.94131i	0.0273084	+	0.137289i
$460$	−8.87797	−	24.5381i	−0.413938	−	1.14410i
$461$	−16.4812	−	24.6659i	−0.767606	−	1.14880i	−0.984972	−	0.172714i	$-0.944746\pi$
$461$	−16.4812	−	24.6659i	−0.767606	−	1.14880i	0.217366	−	0.976090i	$-0.430254\pi$
$462$	1.84328	+	6.61517i	0.0857569	+	0.307766i
$463$	14.2150	−	14.2150i	0.660625	−	0.660625i	−0.294903	−	0.955527i	$-0.595287\pi$
$463$	14.2150	−	14.2150i	0.660625	−	0.660625i	0.955527	+	0.294903i	$0.0952872\pi$
$464$	−1.82090	+	2.25108i	−0.0845330	+	0.104504i
$465$	47.4952	+	47.4952i	2.20254	+	2.20254i
$466$	4.77682	−	8.46717i	0.221282	−	0.392234i
$467$	9.72658	−	6.49909i	0.450093	−	0.300742i	−0.309787	−	0.950806i	$-0.600258\pi$
$467$	9.72658	−	6.49909i	0.450093	−	0.300742i	0.759880	+	0.650064i	$0.225258\pi$
$468$	0.0557137	−	1.22235i	0.00257537	−	0.0565029i
$469$	−12.6607	+	2.51837i	−0.584618	+	0.116288i
$470$	18.0922	−	1.36676i	0.834531	−	0.0630439i
$471$	4.58561	−	11.0706i	0.211294	−	0.510108i
$472$	−15.9798	+	11.3817i	−0.735531	+	0.523884i
$473$	2.33811	+	5.64470i	0.107506	+	0.259543i
$474$	−6.29511	+	3.18267i	−0.289144	+	0.146185i
$475$	33.3929	+	22.3125i	1.53217	+	1.02377i
$476$	−4.70243	−	3.46182i	−0.215535	−	0.158672i
$477$	4.06160	−	20.4190i	0.185968	−	0.934923i
$478$	−2.69502	−	3.44077i	−0.123267	−	0.157377i
$479$			33.3214i			1.52249i	0.648463	+	0.761246i	$0.275412\pi$
$479$			33.3214i			1.52249i	−0.648463	+	0.761246i	$0.724588\pi$
$480$	−53.2848	+	9.73225i	−2.43211	+	0.444214i
$481$		−	2.41238i		−	0.109995i
$482$	−14.3522	+	11.2415i	−0.653725	+	0.512036i
$483$	−2.44978	+	12.3159i	−0.111469	+	0.560391i
$484$	18.8944	−	2.87110i	0.858836	−	0.130505i
$485$	−32.4491	−	21.6818i	−1.47344	−	0.984519i
$486$	−12.1720	−	24.0755i	−0.552134	−	1.09209i
$487$	−8.84785	−	21.3606i	−0.400934	−	0.967941i	−0.987440	−	0.157996i	$-0.949497\pi$
$487$	−8.84785	−	21.3606i	−0.400934	−	0.967941i	0.586505	−	0.809945i	$-0.300503\pi$
$488$	23.6977	+	14.8307i	1.07274	+	0.671355i
$489$	15.8693	−	38.3119i	0.717635	−	1.73252i
$490$	1.72720	+	22.8635i	0.0780271	+	1.03287i
$491$	−16.4921	+	3.28049i	−0.744280	+	0.148046i	−0.552641	−	0.833419i	$-0.686380\pi$
$491$	−16.4921	+	3.28049i	−0.744280	+	0.148046i	−0.191638	+	0.981466i	$0.561380\pi$
$492$	1.34340	−	1.22628i	0.0605651	−	0.0552847i
$493$	−0.991937	+	0.662791i	−0.0446746	+	0.0298506i
$494$	−1.08857	−	0.614125i	−0.0489771	−	0.0276308i
$495$	7.85680	+	7.85680i	0.353137	+	0.353137i
$496$	−13.0514	+	24.8388i	−0.586024	+	1.11529i
$497$	5.81479	−	5.81479i	0.260829	−	0.260829i
$498$	−37.1128	+	10.3412i	−1.66306	+	0.463402i
$499$	−8.82586	−	13.2088i	−0.395100	−	0.591308i	0.579580	−	0.814916i	$-0.303217\pi$
$499$	−8.82586	−	13.2088i	−0.395100	−	0.591308i	−0.974679	+	0.223607i	$0.928217\pi$
$500$	57.9680	+	27.1662i	2.59241	+	1.21491i
$501$	8.63105	+	43.3912i	0.385607	+	1.93858i
$502$	18.1216	−	21.0833i	0.808807	−	0.940994i
$503$	−0.539361	−	0.223411i	−0.0240489	−	0.00996138i	0.370627	−	0.928782i	$-0.379143\pi$
$503$	−0.539361	−	0.223411i	−0.0240489	−	0.00996138i	−0.394675	+	0.918821i	$0.629143\pi$
$504$	10.3157	+	3.91643i	0.459500	+	0.174452i
$505$	−31.6353	+	13.1038i	−1.40775	+	0.583109i
$506$	−5.01855	−	1.64806i	−0.223102	−	0.0732652i
$507$	−16.3754	+	24.5075i	−0.727256	+	1.08842i
$508$	12.1820	+	3.00565i	0.540490	+	0.133354i
$509$	−7.93668	−	1.57870i	−0.351787	−	0.0699748i	0.0160338	−	0.999871i	$-0.494896\pi$
$509$	−7.93668	−	1.57870i	−0.351787	−	0.0699748i	−0.367821	+	0.929897i	$0.619896\pi$
$510$	−22.1555	−	2.69283i	−0.981063	−	0.119240i
$511$	6.50614			0.287814
$512$	−10.4942	−	20.0468i	−0.463781	−	0.885950i
$513$	−5.78845			−0.255566
$514$	22.7520	+	2.76532i	1.00355	+	0.121973i
$515$	25.5559	+	5.08339i	1.12613	+	0.224001i
$516$	22.5154	+	5.55520i	0.991187	+	0.244554i
$517$	2.04047	−	3.05378i	0.0897398	−	0.134305i
$518$	20.6682	+	6.78730i	0.908108	+	0.298217i
$519$	−10.6819	+	4.42461i	−0.468885	+	0.194219i
$520$	−3.08400	−	1.17086i	−0.135243	−	0.0513456i
$521$	0.958515	+	0.397030i	0.0419933	+	0.0173942i	0.403581	−	0.914944i	$-0.367765\pi$
$521$	0.958515	+	0.397030i	0.0419933	+	0.0173942i	−0.361588	+	0.932338i	$0.617765\pi$
$522$	1.46945	−	1.70961i	0.0643161	−	0.0748275i
$523$	−0.257581	−	1.29495i	−0.0112632	−	0.0566240i	0.974745	−	0.223321i	$-0.0716898\pi$
$523$	−0.257581	−	1.29495i	−0.0112632	−	0.0566240i	−0.986008	+	0.166697i	$0.946690\pi$
$524$	27.6118	+	12.9400i	1.20623	+	0.565288i
$525$	−28.3387	−	42.4118i	−1.23680	−	1.85100i
$526$	−33.4327	+	9.31579i	−1.45773	+	0.406188i
$527$	−8.17511	+	8.17511i	−0.356113	+	0.356113i
$528$	−5.10009	+	9.70626i	−0.221953	+	0.422411i
$529$	9.43355	+	9.43355i	0.410154	+	0.410154i
$530$	−48.8841	−	27.5784i	−2.12339	−	1.19793i
$531$	12.7010	−	8.48653i	0.551176	−	0.368284i
$532$	8.32426	−	7.59851i	0.360902	−	0.329437i
$533$	0.108646	−	0.0216110i	0.00470598	−	0.000936077i
$534$	2.42191	+	32.0595i	0.104806	+	1.38735i
$535$	−29.7067	+	71.7183i	−1.28433	+	3.10065i
$536$	−17.4716	−	10.9342i	−0.754657	−	0.472287i
$537$	−15.0363	−	36.3009i	−0.648865	−	1.56650i
$538$	−0.438097	−	0.866528i	−0.0188877	−	0.0373587i
$539$	3.85913	+	2.57859i	0.166224	+	0.111068i
$540$	−15.1043	+	2.29518i	−0.649986	+	0.0987688i
$541$	−0.446774	+	2.24608i	−0.0192083	+	0.0965667i	−0.989200	−	0.146570i	$-0.953177\pi$
$541$	−0.446774	+	2.24608i	−0.0192083	+	0.0965667i	0.969992	+	0.243137i	$0.0781765\pi$
$542$	−15.7749	+	12.3559i	−0.677591	+	0.530730i
$543$		−	24.9626i		−	1.07125i
$544$	−1.67516	−	9.17164i	−0.0718220	−	0.393231i
$545$		−	25.1253i		−	1.07625i
$546$	0.978843	+	1.24971i	0.0418906	+	0.0534825i
$547$	−7.07297	+	35.5582i	−0.302418	+	1.52036i	0.468522	+	0.883452i	$0.344787\pi$
$547$	−7.07297	+	35.5582i	−0.302418	+	1.52036i	−0.770940	+	0.636907i	$0.780213\pi$
$548$	5.89593	+	4.34046i	0.251862	+	0.185415i
$549$	−18.0983	−	12.0929i	−0.772417	−	0.516113i
$550$	19.1488	−	9.68119i	0.816506	−	0.412807i
$551$	−0.881197	−	2.12740i	−0.0375403	−	0.0906302i
$552$	−16.3307	+	11.6316i	−0.695080	+	0.495072i
$553$	1.48249	−	3.57904i	0.0630418	−	0.152196i
$554$	32.7247	−	2.47215i	1.39034	−	0.105032i
$555$	81.5499	−	16.2213i	3.46160	−	0.688555i
$556$	1.95946	−	42.9901i	0.0830996	−	1.82319i
$557$	19.6484	−	13.1287i	0.832531	−	0.556280i	−0.0646672	−	0.997907i	$-0.520599\pi$
$557$	19.6484	−	13.1287i	0.832531	−	0.556280i	0.897199	+	0.441627i	$0.145599\pi$
$558$	10.7346	−	19.0277i	0.454434	−	0.805508i
$559$	0.998673	+	0.998673i	0.0422393	+	0.0422393i
$560$	18.7083	−	23.1281i	0.790571	−	0.977340i
$561$	−3.19459	+	3.19459i	−0.134876	+	0.134876i
$562$	−1.28806	−	4.62260i	−0.0543334	−	0.194993i
$563$	10.2079	+	15.2772i	0.430212	+	0.643858i	0.981724	−	0.190309i	$-0.0609489\pi$
$563$	10.2079	+	15.2772i	0.430212	+	0.643858i	−0.551512	+	0.834167i	$0.685949\pi$
$564$	−4.74285	−	13.1089i	−0.199710	−	0.551984i
$565$	−2.94358	−	14.7984i	−0.123837	−	0.622572i
$566$	−13.2152	−	11.3588i	−0.555478	−	0.477447i
$567$	17.6048	+	7.29216i	0.739333	+	0.306242i
$568$	13.1241	−	0.391911i	0.550675	−	0.0164442i
$569$	32.6965	−	13.5433i	1.37071	−	0.567765i	0.428727	−	0.903434i	$-0.358962\pi$
$569$	32.6965	−	13.5433i	1.37071	−	0.567765i	0.941980	+	0.335669i	$0.108962\pi$
$570$	13.4406	−	40.9282i	0.562964	−	1.71430i
$571$	−9.13934	+	13.6780i	−0.382470	+	0.572406i	−0.971894	−	0.235417i	$-0.924354\pi$
$571$	−9.13934	+	13.6780i	−0.382470	+	0.572406i	0.589425	+	0.807823i	$0.299354\pi$
$572$	−0.571535	+	0.345321i	−0.0238971	+	0.0144386i
$573$	46.2401	+	9.19773i	1.93171	+	0.384241i
$574$	−0.120525	+	0.991631i	−0.00503061	+	0.0413899i
$575$	39.2356			1.63624
$576$	7.70131	+	15.8455i	0.320888	+	0.660229i
$577$	−11.7086			−0.487435			−0.243717	−	0.969846i	$-0.578367\pi$
$577$	−11.7086			−0.487435			−0.243717	+	0.969846i	$0.578367\pi$
$578$	−2.43722	+	20.0525i	−0.101375	+	0.834073i
$579$	−43.9535	−	8.74290i	−1.82665	−	0.363343i
$580$	−3.14292	−	5.20180i	−0.130503	−	0.215993i
$581$	11.7549	−	17.5925i	0.487677	−	0.729861i
$582$	−9.35541	+	28.4884i	−0.387794	+	1.18088i
$583$	−10.4966	+	4.34785i	−0.434726	+	0.180070i
$584$	7.56150	+	7.12299i	0.312897	+	0.294751i
$585$	2.37295	+	0.982908i	0.0981094	+	0.0406383i
$586$	14.6385	+	12.5821i	0.604709	+	0.519762i
$587$	−6.29094	−	31.6267i	−0.259655	−	1.30537i	−0.861906	−	0.507067i	$-0.830730\pi$
$587$	−6.29094	−	31.6267i	−0.259655	−	1.30537i	0.602252	−	0.798306i	$-0.294270\pi$
$588$	16.5660	−	5.99364i	0.683171	−	0.247174i
$589$	−12.3978	−	18.5546i	−0.510841	−	0.764527i
$590$	−11.0538	−	39.6701i	−0.455079	−	1.63319i
$591$	33.0715	−	33.0715i	1.36038	−	1.36038i
$592$	16.5900	+	30.5160i	0.681843	+	1.25420i
$593$	−25.2454	−	25.2454i	−1.03670	−	1.03670i	−0.999300	−	0.0374032i	$-0.988091\pi$
$593$	−25.2454	−	25.2454i	−1.03670	−	1.03670i	−0.0374032	−	0.999300i	$-0.511909\pi$
$594$	−1.51957	+	2.69351i	−0.0623485	+	0.110516i
$595$	10.1914	−	6.80967i	0.417806	−	0.279169i
$596$	−17.5497	−	0.799903i	−0.718863	−	0.0327653i
$597$	−3.04087	+	0.604867i	−0.124455	+	0.0247556i
$598$	−1.21757	+	0.0919804i	−0.0497902	+	0.00376136i
$599$	1.52504	−	3.68178i	0.0623115	−	0.150433i	−0.889657	−	0.456630i	$-0.849056\pi$
$599$	1.52504	−	3.68178i	0.0623115	−	0.150433i	0.951968	+	0.306196i	$0.0990564\pi$
$600$	13.4975	−	80.3170i	0.551031	−	3.27893i
$601$	11.5852	+	27.9691i	0.472570	+	1.14088i	0.963024	+	0.269417i	$0.0868310\pi$
$601$	11.5852	+	27.9691i	0.472570	+	1.14088i	−0.490454	+	0.871467i	$0.663169\pi$
$602$	−11.3660	+	5.74638i	−0.463242	+	0.234205i
$603$	13.3433	+	8.91573i	0.543382	+	0.363077i
$604$	−10.9003	+	14.8066i	−0.443528	+	0.602474i
$605$	−7.82626	+	39.3453i	−0.318183	+	1.59961i
$606$	16.2229	+	20.7121i	0.659011	+	0.841371i
$607$		−	40.9668i		−	1.66279i	−0.555680	−	0.831396i	$-0.687542\pi$
$607$		−	40.9668i		−	1.66279i	0.555680	−	0.831396i	$-0.312458\pi$
$608$	17.9935	+	0.282427i	0.729731	+	0.0114539i
$609$			2.92460i			0.118511i
$610$	−46.1974	+	36.1846i	−1.87048	+	1.46507i
$611$	0.165630	−	0.832680i	0.00670069	−	0.0336866i
$612$	1.09056	+	7.17686i	0.0440834	+	0.290107i
$613$	13.2362	+	8.84413i	0.534604	+	0.357211i	0.793380	−	0.608726i	$-0.208319\pi$
$613$	13.2362	+	8.84413i	0.534604	+	0.357211i	−0.258776	+	0.965937i	$0.583319\pi$
$614$	16.3671	+	32.3730i	0.660521	+	1.30647i
$615$	1.46111	+	3.52742i	0.0589175	+	0.142239i
$616$	−1.35052	−	5.86822i	−0.0544140	−	0.236437i
$617$	−9.10950	+	21.9923i	−0.366735	+	0.885376i	0.627546	+	0.778579i	$0.284059\pi$
$617$	−9.10950	+	21.9923i	−0.366735	+	0.885376i	−0.994281	+	0.106796i	$0.965941\pi$
$618$	−1.50811	−	19.9633i	−0.0606652	−	0.803043i
$619$	−44.5733	+	8.86617i	−1.79155	+	0.356362i	−0.975222	−	0.221227i	$-0.928994\pi$
$619$	−44.5733	+	8.86617i	−1.79155	+	0.356362i	−0.816328	+	0.577589i	$0.803994\pi$
$620$	−39.7076	−	43.5002i	−1.59470	−	1.74701i
$621$	−4.70197	+	3.14176i	−0.188684	+	0.126074i
$622$	−10.9054	−	6.15236i	−0.437266	−	0.246687i
$623$	−12.4853	−	12.4853i	−0.500213	−	0.500213i
$624$	−0.230570	+	2.52407i	−0.00923018	+	0.101044i
$625$	−50.3856	+	50.3856i	−2.01542	+	2.01542i
$626$	4.65156	−	1.29613i	0.185914	−	0.0518036i
$627$	−4.84468	−	7.25058i	−0.193478	−	0.289560i
$628$	−4.45881	+	9.51435i	−0.177926	+	0.379664i
$629$	2.79209	+	14.0368i	0.111328	+	0.559683i
$630$	−15.0975	+	17.5649i	−0.601497	+	0.699803i
$631$	−5.81286	−	2.40776i	−0.231406	−	0.0958516i	0.263967	−	0.964532i	$-0.414969\pi$
$631$	−5.81286	−	2.40776i	−0.231406	−	0.0958516i	−0.495374	+	0.868680i	$0.664969\pi$
$632$	5.64134	−	2.53655i	0.224400	−	0.100899i
$633$	−23.4313	+	9.70558i	−0.931312	+	0.385762i
$634$	23.4984	+	7.71672i	0.933240	+	0.306470i
$635$	−14.6325	+	21.8991i	−0.580674	+	0.869040i
$636$	−10.3302	+	41.8687i	−0.409620	+	1.66020i
$637$	1.05228	+	0.209311i	0.0416927	+	0.00829320i
$638$	−1.22126	−	0.148434i	−0.0483502	−	0.00587658i
$639$	−10.2231			−0.404419
$640$	47.0639	−	6.39763i	1.86036	−	0.252889i
$641$	5.83590			0.230504			0.115252	−	0.993336i	$-0.463232\pi$
$641$	5.83590			0.230504			0.115252	+	0.993336i	$0.463232\pi$
$642$	59.2082	+	7.19628i	2.33676	+	0.284014i
$643$	−44.3564	−	8.82303i	−1.74924	−	0.347946i	−0.786341	−	0.617793i	$-0.788027\pi$
$643$	−44.3564	−	8.82303i	−1.74924	−	0.347946i	−0.962903	+	0.269846i	$0.913027\pi$
$644$	2.63762	−	10.6904i	0.103937	−	0.421260i
$645$	−27.0446	+	40.4751i	−1.06488	+	1.59370i
$646$	7.04477	+	2.31346i	0.277173	+	0.0910218i
$647$	−39.4132	+	16.3255i	−1.54949	+	0.641820i	−0.983224	−	0.182402i	$-0.941613\pi$
$647$	−39.4132	+	16.3255i	−1.54949	+	0.641820i	−0.566267	+	0.824222i	$0.691613\pi$
$648$	12.4770	+	27.7490i	0.490142	+	1.09008i
$649$	−7.70159	−	3.19010i	−0.302314	−	0.125222i
$650$	3.23308	−	3.76147i	0.126812	−	0.147537i
$651$	5.52933	+	27.7978i	0.216711	+	1.08948i
$652$	−15.4305	+	32.9261i	−0.604305	+	1.28949i
$653$	9.71620	+	14.5413i	0.380224	+	0.569046i	0.971386	−	0.237507i	$-0.0763304\pi$
$653$	9.71620	+	14.5413i	0.380224	+	0.569046i	−0.591161	+	0.806553i	$0.701330\pi$
$654$	−18.5963	+	5.18173i	−0.727172	+	0.202622i
$655$	−45.2608	+	45.2608i	−1.76848	+	1.76848i
$656$	−1.22572	+	1.02053i	−0.0478565	+	0.0398451i
$657$	−5.71928	−	5.71928i	−0.223130	−	0.223130i
$658$	6.66801	+	3.76181i	0.259946	+	0.146651i
$659$	15.4630	−	10.3321i	0.602354	−	0.402480i	−0.216665	−	0.976246i	$-0.569518\pi$
$659$	15.4630	−	10.3321i	0.602354	−	0.402480i	0.819019	+	0.573766i	$0.194518\pi$
$660$	−15.5166	−	16.9986i	−0.603982	−	0.661669i
$661$	35.0453	−	6.97094i	1.36310	−	0.271138i	0.541262	−	0.840854i	$-0.317947\pi$
$661$	35.0453	−	6.97094i	1.36310	−	0.271138i	0.821842	+	0.569715i	$0.192947\pi$
$662$	−1.58707	−	21.0085i	−0.0616832	−	0.816519i
$663$	−0.399653	+	0.964847i	−0.0155212	+	0.0374716i
$664$	32.9222	−	7.57676i	1.27763	−	0.294035i
$665$	9.05362	+	21.8574i	0.351084	+	0.847593i
$666$	−12.2021	−	24.1350i	−0.472823	−	0.935213i
$667$	−1.87047	−	1.24981i	−0.0724250	−	0.0483928i
$668$	−5.82803	−	38.3536i	−0.225493	−	1.48394i
$669$	0.177511	−	0.892410i	0.00686299	−	0.0345026i
$670$	34.0599	−	26.6778i	1.31585	−	1.03065i
$671$			11.8786i			0.458569i
$672$	−20.9763	−	9.07695i	−0.809180	−	0.350151i
$673$		−	36.6129i		−	1.41132i	−0.708549	−	0.705662i	$-0.750650\pi$
$673$		−	36.6129i		−	1.41132i	0.708549	−	0.705662i	$-0.249350\pi$
$674$	5.89819	+	7.53031i	0.227190	+	0.290057i
$675$	4.48146	−	22.5298i	0.172492	−	0.867174i
$676$	15.3227	−	20.8138i	0.589333	−	0.800530i
$677$	10.2445	+	6.84516i	0.393728	+	0.263081i	0.736638	−	0.676288i	$-0.236412\pi$
$677$	10.2445	+	6.84516i	0.393728	+	0.263081i	−0.342909	+	0.939368i	$0.611412\pi$
$678$	−10.3458	+	5.23061i	−0.397328	+	0.200880i
$679$	−6.30184	−	15.2140i	−0.241843	−	0.583859i
$680$	19.2998	+	3.24338i	0.740115	+	0.124378i
$681$	10.3742	−	25.0456i	0.397542	−	0.959751i
$682$	−11.8885	+	0.898108i	−0.455235	+	0.0343903i
$683$	32.2106	−	6.40709i	1.23251	−	0.245161i	0.464482	−	0.885583i	$-0.346241\pi$
$683$	32.2106	−	6.40709i	1.23251	−	0.245161i	0.768023	+	0.640422i	$0.221241\pi$
$684$	−13.9971	−	0.637977i	−0.535191	−	0.0243936i
$685$	−12.7780	+	8.53800i	−0.488223	+	0.326220i
$686$	−13.3706	+	23.7001i	−0.510492	+	0.904874i
$687$	11.3919	+	11.3919i	0.434630	+	0.434630i
$688$	−19.5008	−	5.76508i	−0.743462	−	0.219792i
$689$	−1.85709	+	1.85709i	−0.0707495	+	0.0707495i
$690$	−11.2965	−	40.5412i	−0.430052	−	1.54338i
$691$	−12.8884	−	19.2889i	−0.490299	−	0.733785i	0.500995	−	0.865450i	$-0.332967\pi$
$691$	−12.8884	−	19.2889i	−0.490299	−	0.733785i	−0.991294	+	0.131666i	$0.957967\pi$
$692$	9.53361	−	3.44930i	0.362414	−	0.131123i
$693$	0.914678	+	4.59840i	0.0347457	+	0.174679i
$694$	−11.8020	−	10.1441i	−0.447997	−	0.385064i
$695$	83.4571	+	34.5690i	3.16571	+	1.31128i
$696$	−3.20188	+	3.39900i	−0.121367	+	0.128839i
$697$	−0.607158	+	0.251493i	−0.0229977	+	0.00952598i
$698$	−8.76619	+	26.6942i	−0.331805	+	1.01039i
$699$	8.71084	−	13.0367i	0.329474	−	0.493093i
$700$	23.1302	+	38.2825i	0.874241	+	1.44694i
$701$	7.52527	+	1.49687i	0.284226	+	0.0565360i	0.335144	−	0.942167i	$-0.391215\pi$
$701$	7.52527	+	1.49687i	0.284226	+	0.0565360i	−0.0509187	+	0.998703i	$0.516215\pi$
$702$	−0.0862535	+	0.709660i	−0.00325543	+	0.0267844i
$703$	−27.6242			−1.04186
$704$	4.85501	−	8.29867i	0.182980	−	0.312768i
$705$	29.2622			1.10208
$706$	3.87607	−	31.8908i	0.145878	−	1.20023i
$707$	−14.1711	−	2.81880i	−0.532957	−	0.106012i
$708$	−27.0818	+	16.3628i	−1.01780	+	0.614950i
$709$	10.0146	−	14.9879i	0.376106	−	0.562883i	−0.594336	−	0.804217i	$-0.702585\pi$
$709$	10.0146	−	14.9879i	0.376106	−	0.562883i	0.970442	+	0.241334i	$0.0775850\pi$
$710$	−8.59899	+	26.1850i	−0.322714	+	0.982706i
$711$	−4.44938	+	1.84299i	−0.166865	+	0.0691177i
$712$	−0.841496	−	28.1796i	−0.0315364	−	1.05607i
$713$	−20.1415	−	8.34287i	−0.754304	−	0.312443i
$714$	−7.14194	−	6.13867i	−0.267280	−	0.229734i
$715$	−0.273453	−	1.37474i	−0.0102266	−	0.0514124i
$716$	11.7219	+	32.3984i	0.438067	+	1.21079i
$717$	−3.91614	−	5.86092i	−0.146251	−	0.218880i
$718$	−13.8933	−	49.8607i	−0.518495	−	1.86078i
$719$	10.5187	−	10.5187i	0.392280	−	0.392280i	−0.483219	−	0.875499i	$-0.660533\pi$
$719$	10.5187	−	10.5187i	0.392280	−	0.392280i	0.875499	+	0.483219i	$0.160533\pi$
$720$	−36.7767	+	3.88525i	−1.37059	+	0.144795i
$721$	7.77454	+	7.77454i	0.289539	+	0.289539i
$722$	6.17048	−	10.9375i	0.229641	−	0.407052i
$723$	−24.4472	+	16.3351i	−0.909201	+	0.607508i
$724$	−0.996649	+	21.8662i	−0.0370402	+	0.812653i
$725$	8.96250	−	1.78275i	0.332859	−	0.0662097i
$726$	30.7351	−	2.32185i	1.14069	−	0.0861720i
$727$	12.9735	−	31.3209i	0.481162	−	1.16163i	−0.477896	−	0.878416i	$-0.658600\pi$
$727$	12.9735	−	31.3209i	0.481162	−	1.16163i	0.959058	−	0.283211i	$-0.0913996\pi$
$728$	−0.807532	−	1.13377i	−0.0299291	−	0.0420204i
$729$	−4.30086	−	10.3832i	−0.159291	−	0.384563i
$730$	−19.4598	+	9.83845i	−0.720240	+	0.364138i
$731$	−6.96677	−	4.65505i	−0.257675	−	0.172173i
$732$	36.3092	+	26.7300i	1.34203	+	0.987971i
$733$	−4.66780	+	23.4666i	−0.172409	+	0.866759i	0.793637	+	0.608391i	$0.208185\pi$
$733$	−4.66780	+	23.4666i	−0.172409	+	0.866759i	−0.966047	+	0.258368i	$0.916815\pi$
$734$	−13.1211	−	16.7519i	−0.484308	−	0.618324i
$735$			36.9793i			1.36400i
$736$	14.7694	−	9.53678i	0.544408	−	0.351530i
$737$		−	8.75773i		−	0.322595i
$738$	0.977651	−	0.765754i	0.0359878	−	0.0281878i
$739$	4.30057	−	21.6204i	0.158199	−	0.795320i	−0.817453	−	0.575996i	$-0.804615\pi$
$739$	4.30057	−	21.6204i	0.158199	−	0.795320i	0.975652	−	0.219325i	$-0.0703854\pi$
$740$	−72.0821	+	10.9533i	−2.64979	+	0.402650i
$741$	−1.67604	−	1.11990i	−0.0615710	−	0.0411404i
$742$	−10.6857	−	21.1357i	−0.392285	−	0.775914i
$743$	−1.75751	−	4.24301i	−0.0644769	−	0.155661i	0.888357	−	0.459154i	$-0.151847\pi$
$743$	−1.75751	−	4.24301i	−0.0644769	−	0.155661i	−0.952834	+	0.303493i	$0.901847\pi$
$744$	−24.0071	+	38.3605i	−0.880144	+	1.40636i
$745$	14.1120	−	34.0694i	0.517024	−	1.24821i
$746$	−0.517113	−	6.84518i	−0.0189328	−	0.250620i
$747$	−25.7982	+	5.13158i	−0.943906	+	0.187755i
$748$	2.92588	−	2.67079i	0.106981	−	0.0976537i
$749$	−27.2354	+	18.1981i	−0.995158	+	0.664944i
$750$	89.9246	+	50.7317i	3.28358	+	1.85246i
$751$	25.9585	+	25.9585i	0.947238	+	0.947238i	0.998676	−	0.0514384i	$-0.0163806\pi$
$751$	25.9585	+	25.9585i	0.947238	+	0.947238i	−0.0514384	+	0.998676i	$0.516381\pi$
$752$	3.63116	+	11.6722i	0.132415	+	0.425643i
$753$	31.7049	−	31.7049i	1.15539	−	1.15539i
$754$	−0.273948	+	0.0763339i	−0.00997661	+	0.00277992i
$755$	−21.4418	−	32.0899i	−0.780346	−	1.16787i
$756$	−5.83737	−	2.73563i	−0.212303	−	0.0994938i
$757$	−1.73528	−	8.72382i	−0.0630697	−	0.317073i	0.936353	−	0.351061i	$-0.114179\pi$
$757$	−1.73528	−	8.72382i	−0.0630697	−	0.317073i	−0.999422	+	0.0339884i	$0.989179\pi$
$758$	7.12596	−	8.29059i	0.258826	−	0.301128i
$759$	−7.87069	−	3.26015i	−0.285688	−	0.118336i
$760$	−13.4075	+	35.3149i	−0.486341	+	1.28101i
$761$	27.8964	−	11.5551i	1.01124	−	0.418871i	0.185336	−	0.982675i	$-0.440663\pi$
$761$	27.8964	−	11.5551i	1.01124	−	0.418871i	0.825909	+	0.563804i	$0.190663\pi$
$762$	19.2262	+	6.31375i	0.696491	+	0.228723i
$763$	5.89011	−	8.81517i	0.213236	−	0.319130i
$764$	−40.1372	−	9.90301i	−1.45211	−	0.358278i
$765$	−14.9449	−	2.97273i	−0.540336	−	0.107479i
$766$	18.6188	+	2.26296i	0.672724	+	0.0817642i
$767$	−1.92698			−0.0695793
$768$	−14.4414	−	33.5145i	−0.521108	−	1.20935i
$769$	17.7614			0.640492			0.320246	−	0.947334i	$-0.396234\pi$
$769$	17.7614			0.640492			0.320246	+	0.947334i	$0.396234\pi$
$770$	12.5475	+	1.52505i	0.452181	+	0.0549590i
$771$	36.2542	+	7.21140i	1.30566	+	0.259712i
$772$	38.1525	+	9.41331i	1.37314	+	0.338792i
$773$	18.1617	−	27.1809i	0.653230	−	0.977627i	−0.345994	−	0.938237i	$-0.612458\pi$
$773$	18.1617	−	27.1809i	0.653230	−	0.977627i	0.999224	−	0.0393906i	$-0.0125417\pi$
$774$	15.0428	+	4.93995i	0.540701	+	0.177563i
$775$	81.8166	−	33.8895i	2.93894	−	1.21735i
$776$	9.33238	−	24.5812i	0.335013	−	0.882413i
$777$	32.4143	+	13.4264i	1.16286	+	0.481671i
$778$	−11.8016	+	13.7304i	−0.423107	+	0.492258i
$779$	−0.247467	−	1.24410i	−0.00886643	−	0.0445746i
$780$	−4.81750	−	2.25767i	−0.172494	−	0.0808377i
$781$	3.09952	+	4.63876i	0.110910	+	0.165988i
$782$	6.97815	−	1.94442i	0.249538	−	0.0695322i
$783$	−0.931310	+	0.931310i	−0.0332823	+	0.0332823i
$784$	−14.7505	+	4.58878i	−0.526802	+	0.163885i
$785$	−15.5957	−	15.5957i	−0.556636	−	0.556636i
$786$	42.8337	+	24.1649i	1.52783	+	0.861935i
$787$	20.5749	−	13.7477i	0.733416	−	0.490053i	−0.131911	−	0.991262i	$-0.542111\pi$
$787$	20.5749	−	13.7477i	0.733416	−	0.490053i	0.865326	+	0.501209i	$0.167111\pi$
$788$	−30.2897	+	27.6489i	−1.07903	+	0.984951i
$789$	−54.8987	+	10.9200i	−1.95445	+	0.388763i
$790$	0.978045	+	12.9467i	0.0347973	+	0.460622i
$791$	2.43642	−	5.88203i	0.0866290	−	0.209141i
$792$	−3.97133	+	6.34570i	−0.141115	+	0.225485i
$793$	1.05080	+	2.53684i	0.0373148	+	0.0900860i
$794$	−25.0063	−	49.4607i	−0.887439	−	1.75530i
$795$	−75.2657	−	50.2909i	−2.66940	−	1.78364i
$796$	2.68783	−	0.408430i	0.0952677	−	0.0144764i
$797$	0.0956446	−	0.480838i	0.00338791	−	0.0170322i	−0.979054	−	0.203599i	$-0.934736\pi$
$797$	0.0956446	−	0.480838i	0.00338791	−	0.0170322i	0.982442	+	0.186567i	$0.0597361\pi$
$798$	14.3104	−	11.2087i	0.506581	−	0.396784i
$799$			5.03676i			0.178188i
$800$	−15.0299	+	69.8156i	−0.531389	+	2.46835i
$801$			21.9506i			0.775587i
$802$	−2.21863	−	2.83256i	−0.0783424	−	0.100021i
$803$	−0.861124	+	4.32916i	−0.0303884	+	0.152773i
$804$	−26.7696	−	19.7072i	−0.944093	−	0.695021i
$805$	19.2177	+	12.8408i	0.677334	+	0.452580i
$806$	−2.45951	+	1.24348i	−0.0866327	+	0.0437996i
$807$	−0.599279	−	1.44679i	−0.0210956	−	0.0509294i
$808$	−13.3837	−	18.7907i	−0.470837	−	0.661053i
$809$	−20.2707	+	48.9378i	−0.712680	+	1.72056i	−0.0194867	+	0.999810i	$0.506203\pi$
$809$	−20.2707	+	48.9378i	−0.712680	+	1.72056i	−0.693193	+	0.720752i	$0.743797\pi$
$810$	−63.6830	+	4.81087i	−2.23759	+	0.169037i
$811$	−1.17029	+	0.232786i	−0.0410945	+	0.00817421i	−0.215595	−	0.976483i	$-0.569169\pi$
$811$	−1.17029	+	0.232786i	−0.0410945	+	0.00817421i	0.174500	+	0.984657i	$0.444169\pi$
$812$	0.116767	−	2.56183i	0.00409770	−	0.0899026i
$813$	−26.8706	+	17.9544i	−0.942394	+	0.629687i
$814$	−7.25180	+	12.8542i	−0.254176	+	0.450540i
$815$	−53.9718	−	53.9718i	−1.89055	−	1.89055i
$816$	−1.57975	−	14.9535i	−0.0553024	−	0.523477i
$817$	11.4358	−	11.4358i	0.400087	−	0.400087i
$818$	2.62347	+	9.41516i	0.0917276	+	0.329193i
$819$	0.602122	+	0.901139i	0.0210398	+	0.0314883i
$820$	−1.13904	−	3.14822i	−0.0397769	−	0.109941i
$821$	5.87139	+	29.5175i	0.204913	+	1.03017i	0.937099	+	0.349062i	$0.113500\pi$
$821$	5.87139	+	29.5175i	0.204913	+	1.03017i	−0.732187	+	0.681104i	$0.761500\pi$
$822$	8.95460	+	7.69669i	0.312328	+	0.268453i
$823$	−28.7325	−	11.9014i	−1.00155	−	0.414857i	−0.179187	−	0.983815i	$-0.557347\pi$
$823$	−28.7325	−	11.9014i	−1.00155	−	0.414857i	−0.822366	+	0.568958i	$0.807347\pi$
$824$	0.523996	+	17.5473i	0.0182543	+	0.611289i
$825$	31.9715	−	13.2430i	1.11311	−	0.461063i
$826$	5.42162	−	16.5095i	0.188642	−	0.574439i
$827$	−2.10263	+	3.14680i	−0.0731155	+	0.109425i	−0.866225	−	0.499654i	$-0.833461\pi$
$827$	−2.10263	+	3.14680i	−0.0731155	+	0.109425i	0.793110	+	0.609079i	$0.208461\pi$
$828$	−11.7161	+	7.07886i	−0.407163	+	0.246007i
$829$	25.7896	+	5.12986i	0.895709	+	0.178168i	0.621418	−	0.783479i	$-0.286557\pi$
$829$	25.7896	+	5.12986i	0.895709	+	0.178168i	0.274291	+	0.961647i	$0.411557\pi$
$830$	−8.55591	+	70.3948i	−0.296980	+	2.44344i
$831$	52.9287			1.83607
$832$	0.302745	−	2.20178i	0.0104958	−	0.0763329i
$833$	−6.36507			−0.220536
$834$	8.37415	−	68.8993i	0.289973	−	2.38579i
$835$	79.8666	+	15.8865i	2.76390	+	0.549774i
$836$	3.95426	+	6.54464i	0.136761	+	0.226351i
$837$	−7.09119	+	10.6127i	−0.245107	+	0.366829i
$838$	2.53781	−	7.72796i	0.0876673	−	0.266958i
$839$	21.7694	−	9.01718i	0.751563	−	0.311308i	0.0261841	−	0.999657i	$-0.491664\pi$
$839$	21.7694	−	9.01718i	0.751563	−	0.311308i	0.725379	+	0.688349i	$0.241664\pi$
$840$	32.8969	−	34.9221i	1.13505	−	1.20493i
$841$	26.3085	+	10.8973i	0.907188	+	0.375770i
$842$	−28.3621	−	24.3779i	−0.977424	−	0.840119i
$843$	−1.50987	−	7.59062i	−0.0520026	−	0.261435i
$844$	20.9124	−	7.56619i	0.719835	−	0.260439i
$845$	30.1408	+	45.1089i	1.03688	+	1.55179i
$846$	−2.55473	−	9.16844i	−0.0878333	−	0.315217i
$847$	−11.9695	+	11.9695i	−0.411276	+	0.411276i
$848$	10.7205	−	36.2629i	0.368143	−	1.24527i
$849$	−19.8730	−	19.8730i	−0.682038	−	0.682038i
$850$	−14.4586	+	25.6286i	−0.495925	+	0.879054i
$851$	−22.4392	+	14.9934i	−0.769205	+	0.513966i
$852$	21.1540	+	0.964186i	0.724724	+	0.0330325i
$853$	−13.0606	+	2.59791i	−0.447186	+	0.0889509i	−0.413546	−	0.910483i	$-0.635710\pi$
$853$	−13.0606	+	2.59791i	−0.447186	+	0.0889509i	−0.0336401	+	0.999434i	$0.510710\pi$
$854$	−24.6910	+	1.86526i	−0.844907	+	0.0638277i
$855$	11.2553	−	27.1726i	0.384922	−	0.929284i
$856$	−51.5767	−	8.66758i	−1.76285	−	0.296252i
$857$	−13.3651	−	32.2661i	−0.456542	−	1.10219i	−0.969788	−	0.243948i	$-0.921557\pi$
$857$	−13.3651	−	32.2661i	−0.456542	−	1.10219i	0.513246	−	0.858241i	$-0.328443\pi$
$858$	−0.961106	+	0.485914i	−0.0328116	+	0.0165888i
$859$	3.86744	+	2.58414i	0.131955	+	0.0881697i	0.619796	−	0.784763i	$-0.287215\pi$
$859$	3.86744	+	2.58414i	0.131955	+	0.0881697i	−0.487841	+	0.872933i	$0.662215\pi$
$860$	25.3060	−	34.3748i	0.862926	−	1.17217i
$861$	−0.314304	+	1.58011i	−0.0107115	+	0.0538501i
$862$	6.98880	+	8.92272i	0.238040	+	0.303909i
$863$			9.50850i			0.323673i	0.986818	+	0.161837i	$0.0517418\pi$
$863$			9.50850i			0.323673i	−0.986818	+	0.161837i	$0.948258\pi$
$864$	−3.78925	−	9.57019i	−0.128913	−	0.325584i
$865$			21.2813i			0.723587i
$866$	14.8486	−	11.6303i	0.504574	−	0.395213i
$867$	−6.35577	+	31.9526i	−0.215853	+	1.08517i
$868$	−3.73362	−	24.5705i	−0.126727	−	0.833978i
$869$	2.18527	+	1.46015i	0.0741301	+	0.0495322i
$870$	−4.42252	−	8.74745i	−0.149937	−	0.296566i
$871$	−0.774719	−	1.87034i	−0.0262504	−	0.0633740i
$872$	16.4965	−	3.79652i	0.558641	−	0.128566i
$873$	−7.83431	+	18.9137i	−0.265151	+	0.640132i
$874$	1.05327	+	13.9424i	0.0356272	+	0.471609i
$875$	−55.6130	+	11.0621i	−1.88006	+	0.373968i
$876$	11.2951	+	12.3740i	0.381627	+	0.418077i
$877$	−16.1414	+	10.7854i	−0.545058	+	0.364196i	−0.797408	−	0.603440i	$-0.793796\pi$
$877$	−16.1414	+	10.7854i	−0.545058	+	0.364196i	0.252351	+	0.967636i	$0.418796\pi$
$878$	25.3452	+	14.2987i	0.855360	+	0.482558i
$879$	22.0132	+	22.0132i	0.742486	+	0.742486i
$880$	12.9132	+	15.5096i	0.435304	+	0.522828i
$881$	18.1256	−	18.1256i	0.610667	−	0.610667i	−0.332453	−	0.943120i	$-0.607876\pi$
$881$	18.1256	−	18.1256i	0.610667	−	0.610667i	0.943120	+	0.332453i	$0.107876\pi$
$882$	11.5864	−	3.22846i	0.390133	−	0.108708i
$883$	25.2429	+	37.7787i	0.849491	+	1.27135i	0.960709	+	0.277557i	$0.0895249\pi$
$883$	25.2429	+	37.7787i	0.849491	+	1.27135i	−0.111218	+	0.993796i	$0.535475\pi$
$884$	0.388602	−	0.829211i	0.0130701	−	0.0278894i
$885$	−12.9574	−	65.1411i	−0.435557	−	2.18969i
$886$	−16.3623	+	19.0364i	−0.549701	+	0.639541i
$887$	−36.7160	−	15.2083i	−1.23280	−	0.510644i	−0.331345	−	0.943510i	$-0.607502\pi$
$887$	−36.7160	−	15.2083i	−1.23280	−	0.510644i	−0.901458	+	0.432866i	$0.857502\pi$
$888$	22.9728	+	51.0919i	0.770917	+	1.71453i
$889$	−10.2676	+	4.25297i	−0.344363	+	0.142640i
$890$	56.2235	+	18.4634i	1.88462	+	0.618896i
$891$	−7.18228	+	10.7490i	−0.240615	+	0.360106i
$892$	−0.191123	+	0.774628i	−0.00639927	+	0.0259365i
$893$	−9.53500	−	1.89663i	−0.319077	−	0.0634683i
$894$	−28.1265	−	3.41855i	−0.940691	−	0.114333i
$895$	−72.3211			−2.41743
$896$	18.0120	+	8.78854i	0.601740	+	0.293604i
$897$	−1.96929			−0.0657528
$898$	−18.0534	−	2.19424i	−0.602449	−	0.0732228i
$899$	−4.97995	−	0.990574i	−0.166091	−	0.0330375i
$900$	13.3198	−	53.9855i	0.443992	−	1.79952i
$901$	8.65633	−	12.9551i	0.288384	−	0.431597i
$902$	−0.643876	−	0.211445i	−0.0214387	−	0.00704034i
$903$	−18.9770	+	7.86055i	−0.631517	+	0.261583i
$904$	9.27134	−	4.16874i	0.308360	−	0.138650i
$905$	−42.4491	−	17.5830i	−1.41106	−	0.584479i
$906$	−19.3290	+	22.4880i	−0.642162	+	0.747113i
$907$	5.87925	+	29.5570i	0.195217	+	0.981424i	0.946809	+	0.321796i	$0.104286\pi$
$907$	5.87925	+	29.5570i	0.195217	+	0.981424i	−0.751592	+	0.659628i	$0.770714\pi$
$908$	−10.0874	+	21.5248i	−0.334762	+	0.714325i
$909$	9.97931	+	14.9351i	0.330993	+	0.495366i
$910$	2.81461	−	0.784272i	0.0933033	−	0.0259984i
$911$	16.2630	−	16.2630i	0.538818	−	0.538818i	−0.384364	−	0.923182i	$-0.625579\pi$
$911$	16.2630	−	16.2630i	0.538818	−	0.538818i	0.923182	+	0.384364i	$0.125579\pi$
$912$	28.9031	+	2.64025i	0.957076	+	0.0874274i
$913$	10.1502	+	10.1502i	0.335922	+	0.335922i
$914$	−6.15383	−	3.47173i	−0.203551	−	0.114835i
$915$	−78.6915	+	52.5800i	−2.60146	+	1.73824i
$916$	−9.52405	−	10.4337i	−0.314684	−	0.344740i
$917$	−26.4901	+	5.26920i	−0.874779	+	0.174004i
$918$	−0.319482	−	4.22908i	−0.0105445	−	0.139580i
$919$	−6.05005	+	14.6061i	−0.199573	+	0.481811i	−0.991704	−	0.128539i	$-0.958971\pi$
$919$	−6.05005	+	14.6061i	−0.199573	+	0.481811i	0.792132	+	0.610350i	$0.208971\pi$
$920$	8.27668	+	35.9635i	0.272874	+	1.18568i
$921$	22.3887	+	54.0512i	0.737734	+	1.78105i
$922$	18.9289	+	37.4402i	0.623391	+	1.23303i
$923$	1.07230	+	0.716486i	0.0352951	+	0.0235834i
$924$	−1.45899	−	9.60144i	−0.0479973	−	0.315864i
$925$	21.3868	−	107.519i	0.703195	−	3.53520i
$926$	−22.3816	+	17.5306i	−0.735506	+	0.576092i
$927$		−	13.6686i		−	0.448935i
$928$	2.94043	−	2.84955i	0.0965243	−	0.0935410i
$929$			15.1489i			0.497021i	0.968629	+	0.248510i	$0.0799410\pi$
$929$			15.1489i			0.497021i	−0.968629	+	0.248510i	$0.920059\pi$
$930$	−58.5735	−	74.7818i	−1.92070	−	2.45219i
$931$	2.39681	−	12.0496i	0.0785524	−	0.394910i
$932$	−8.15085	+	11.0718i	−0.266990	+	0.362670i
$933$	−16.7908	−	11.2192i	−0.549705	−	0.367301i
$934$	−14.7639	+	7.46431i	−0.483090	+	0.244240i
$935$	3.18225	+	7.68262i	0.104071	+	0.251249i
$936$	−0.286785	+	1.70652i	−0.00937386	+	0.0557794i
$937$	−16.5832	+	40.0355i	−0.541751	+	1.30790i	0.381736	+	0.924271i	$0.375326\pi$
$937$	−16.5832	+	40.0355i	−0.541751	+	1.30790i	−0.923487	+	0.383630i	$0.874674\pi$
$938$	18.2039	−	1.37520i	0.594378	−	0.0449017i
$939$	7.63818	−	1.51933i	0.249262	−	0.0495814i
$940$	−25.6325	−	1.16831i	−0.836041	−	0.0381062i
$941$	47.9669	−	32.0505i	1.56368	−	1.04481i	0.592765	−	0.805376i	$-0.298036\pi$
$941$	47.9669	−	32.0505i	1.56368	−	1.04481i	0.970911	−	0.239439i	$-0.0769636\pi$
$942$	−8.32664	+	14.7594i	−0.271297	+	0.480888i
$943$	−0.876271	−	0.876271i	−0.0285353	−	0.0285353i
$944$	24.3758	−	13.2519i	0.793366	−	0.431312i
$945$	9.56849	−	9.56849i	0.311263	−	0.311263i
$946$	−2.31927	−	8.32344i	−0.0754061	−	0.270618i
$947$	−4.70450	−	7.04078i	−0.152876	−	0.228794i	0.747125	−	0.664684i	$-0.231434\pi$
$947$	−4.70450	−	7.04078i	−0.152876	−	0.228794i	−0.900000	+	0.435890i	$0.856434\pi$
$948$	9.38065	−	3.39395i	0.304669	−	0.110230i
$949$	0.199058	+	1.00073i	0.00646168	+	0.0324851i
$950$	−43.0726	−	37.0219i	−1.39746	−	1.20115i
$951$	36.8530	+	15.2650i	1.19504	+	0.495001i
$952$	6.01096	+	5.66237i	0.194816	+	0.183519i
$953$	−19.9974	+	8.28320i	−0.647780	+	0.268319i	−0.682286	−	0.731085i	$-0.739014\pi$
$953$	−19.9974	+	8.28320i	−0.647780	+	0.268319i	0.0345063	+	0.999404i	$0.489014\pi$
$954$	−9.18611	+	27.9729i	−0.297411	+	0.905655i
$955$	48.2111	−	72.1531i	1.56008	−	2.33482i
$956$	3.19638	+	5.29029i	0.103378	+	0.171100i
$957$	−1.94602	−	0.387087i	−0.0629058	−	0.0125127i
$958$	5.68565	−	46.7793i	0.183695	−	1.51137i
$959$	−6.48469			−0.209402
$960$	76.4661	−	4.57093i	2.46793	−	0.147526i
$961$	−18.2064			−0.587304
$962$	−0.411626	+	3.38670i	−0.0132714	+	0.109192i
$963$	39.9387	+	7.94430i	1.28701	+	0.256002i
$964$	22.0669	−	13.3328i	0.710729	−	0.429421i
$965$	−45.8271	+	68.5851i	−1.47523	+	2.20783i
$966$	5.54066	−	16.8720i	0.178268	−	0.542848i
$967$	−4.47791	+	1.85481i	−0.144000	+	0.0596467i	−0.453519	−	0.891246i	$-0.649832\pi$
$967$	−4.47791	+	1.85481i	−0.144000	+	0.0596467i	0.309520	+	0.950893i	$0.399832\pi$
$968$	−27.0154	+	0.806731i	−0.868307	+	0.0259293i
$969$	11.0484	+	4.57642i	0.354927	+	0.147016i
$970$	41.8551	+	35.9755i	1.34389	+	1.15510i
$971$	9.90954	+	49.8186i	0.318012	+	1.59876i	0.727280	+	0.686341i	$0.240784\pi$
$971$	9.90954	+	49.8186i	0.318012	+	1.59876i	−0.409268	+	0.912414i	$0.634216\pi$
$972$	12.9801	+	35.8760i	0.416336	+	1.15072i
$973$	21.1767	+	31.6932i	0.678895	+	1.01604i
$974$	8.77657	+	31.4975i	0.281219	+	1.00924i
$975$	5.65647	−	5.65647i	0.181152	−	0.181152i
$976$	−30.7382	−	24.8641i	−0.983905	−	0.795881i
$977$	−26.9502	−	26.9502i	−0.862215	−	0.862215i	0.129380	−	0.991595i	$-0.458701\pi$
$977$	−26.9502	−	26.9502i	−0.862215	−	0.862215i	−0.991595	+	0.129380i	$0.958701\pi$
$978$	−28.8158	+	51.0776i	−0.921428	+	1.63328i
$979$	9.96018	−	6.65518i	0.318329	−	0.212700i
$980$	1.47642	−	32.3924i	0.0471627	−	1.03474i
$981$	−12.9268	+	2.57130i	−0.412721	+	0.0820953i
$982$	23.7128	−	1.79136i	0.756705	−	0.0571646i
$983$	5.35576	−	12.9300i	0.170822	−	0.412402i	−0.815163	−	0.579231i	$-0.803353\pi$
$983$	5.35576	−	12.9300i	0.170822	−	0.412402i	0.985986	+	0.166829i	$0.0533529\pi$
$984$	−2.09521	+	1.49232i	−0.0667930	+	0.0475734i
$985$	−32.9436	−	79.5330i	−1.04967	−	2.53413i
$986$	1.50566	−	0.761226i	0.0479498	−	0.0242424i
$987$	10.2666	+	6.85991i	0.326789	+	0.218353i
$988$	1.42343	+	1.04790i	0.0452855	+	0.0333382i
$989$	3.08239	−	15.4962i	0.0980144	−	0.492752i
$990$	−9.68941	−	12.3706i	−0.307950	−	0.393164i
$991$			45.6448i			1.44996i	0.688772	+	0.724978i	$0.258150\pi$
$991$			45.6448i			1.44996i	−0.688772	+	0.724978i	$0.741850\pi$
$992$	22.5608	−	32.6437i	0.716307	−	1.03644i
$993$		−	33.9790i		−	1.07829i
$994$	−9.15546	+	7.17110i	−0.290394	+	0.227453i
$995$	−1.11333	+	5.59708i	−0.0352949	+	0.177439i
$996$	53.8665	−	8.18531i	1.70683	−	0.259361i
$997$	25.8151	+	17.2491i	0.817572	+	0.546284i	0.892575	−	0.450899i	$-0.148897\pi$
$997$	25.8151	+	17.2491i	0.817572	+	0.546284i	−0.0750031	+	0.997183i	$0.523897\pi$
$998$	10.1366	+	20.0496i	0.320869	+	0.634659i
$999$	6.04651	+	14.5976i	0.191303	+	0.461846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.29.1	✓	56
3.2	odd	2		576.2.bd.a.541.7		56
4.3	odd	2		256.2.i.a.209.6		56
8.3	odd	2		512.2.i.a.161.2		56
8.5	even	2		512.2.i.b.161.6		56
64.11	odd	16		256.2.i.a.49.6		56
64.21	even	16		512.2.i.b.353.6		56
64.43	odd	16		512.2.i.a.353.2		56
64.53	even	16	inner	64.2.i.a.53.1	yes	56
192.53	odd	16		576.2.bd.a.181.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.1	✓	56	1.1	even	1	trivial
64.2.i.a.53.1	yes	56	64.53	even	16	inner
256.2.i.a.49.6		56	64.11	odd	16
256.2.i.a.209.6		56	4.3	odd	2
512.2.i.a.161.2		56	8.3	odd	2
512.2.i.a.353.2		56	64.43	odd	16
512.2.i.b.161.6		56	8.5	even	2
512.2.i.b.353.6		56	64.21	even	16
576.2.bd.a.181.7		56	192.53	odd	16
576.2.bd.a.541.7		56	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40388 - 0.170631i) q^{2} +(-2.23702 - 0.444970i) q^{3} +(1.94177 + 0.479090i) q^{4} +(-2.33237 + 3.49064i) q^{5} +(3.06458 + 1.00639i) q^{6} +(-1.63661 + 0.677907i) q^{7} +(-2.64427 - 1.00391i) q^{8} +(2.03460 + 0.842759i) q^{9} +O(q^{10})\)	\(q+(-1.40388 - 0.170631i) q^{2} +(-2.23702 - 0.444970i) q^{3} +(1.94177 + 0.479090i) q^{4} +(-2.33237 + 3.49064i) q^{5} +(3.06458 + 1.00639i) q^{6} +(-1.63661 + 0.677907i) q^{7} +(-2.64427 - 1.00391i) q^{8} +(2.03460 + 0.842759i) q^{9} +(3.86998 - 4.50247i) q^{10} +(-0.234463 - 1.17872i) q^{11} +(-4.13059 - 1.93576i) q^{12} +(-0.154344 - 0.230992i) q^{13} +(2.41328 - 0.672446i) q^{14} +(6.77078 - 6.77078i) q^{15} +(3.54094 + 1.86057i) q^{16} +(1.16542 + 1.16542i) q^{17} +(-2.71254 - 1.53030i) q^{18} +(-2.64509 + 1.76739i) q^{19} +(-6.20126 + 5.66061i) q^{20} +(3.96278 - 0.788246i) q^{21} +(0.128032 + 1.69479i) q^{22} +(-1.18934 + 2.87131i) q^{23} +(5.46856 + 3.42239i) q^{24} +(-4.83120 - 11.6635i) q^{25} +(0.177266 + 0.350621i) q^{26} +(1.51292 + 1.01090i) q^{27} +(-3.50271 + 0.532255i) q^{28} +(-0.141213 + 0.709928i) q^{29} +(-10.6607 + 8.35008i) q^{30} +7.01473i q^{31} +(-4.65360 - 3.21621i) q^{32} +2.74115i q^{33} +(-1.43726 - 1.83497i) q^{34} +(1.45086 - 7.29396i) q^{35} +(3.54697 + 2.61120i) q^{36} +(7.22008 + 4.82430i) q^{37} +(4.01496 - 2.02987i) q^{38} +(0.242485 + 0.585411i) q^{39} +(9.67171 - 6.88870i) q^{40} +(-0.152591 + 0.368387i) q^{41} +(-5.69777 + 0.430433i) q^{42} +(-4.98611 + 0.991798i) q^{43} +(0.109442 - 2.40114i) q^{44} +(-7.68722 + 5.13643i) q^{45} +(2.15962 - 3.82804i) q^{46} +(2.16092 + 2.16092i) q^{47} +(-7.09325 - 5.73773i) q^{48} +(-2.73080 + 2.73080i) q^{49} +(4.79227 + 17.1986i) q^{50} +(-2.08849 - 3.12564i) q^{51} +(-0.189034 - 0.522478i) q^{52} +(-1.84431 - 9.27195i) q^{53} +(-1.95147 - 1.67733i) q^{54} +(4.66135 + 1.93079i) q^{55} +(5.00821 - 0.149555i) q^{56} +(6.70353 - 2.77669i) q^{57} +(0.319382 - 0.972559i) q^{58} +(3.85360 - 5.76732i) q^{59} +(16.3911 - 9.90349i) q^{60} +(-9.69397 - 1.92825i) q^{61} +(1.19693 - 9.84785i) q^{62} -3.90117 q^{63} +(5.98432 + 5.30923i) q^{64} +1.16630 q^{65} +(0.467724 - 3.84825i) q^{66} +(7.14707 + 1.42164i) q^{67} +(1.70464 + 2.82132i) q^{68} +(3.93821 - 5.89395i) q^{69} +(-3.28141 + 9.99230i) q^{70} +(-4.28878 + 1.77647i) q^{71} +(-4.53398 - 4.27104i) q^{72} +(-3.39319 - 1.40550i) q^{73} +(-9.31297 - 8.00472i) q^{74} +(5.61753 + 28.2413i) q^{75} +(-5.98289 + 2.16463i) q^{76} +(1.18279 + 1.77017i) q^{77} +(-0.240532 - 0.863224i) q^{78} +(-1.54634 + 1.54634i) q^{79} +(-14.7534 + 8.02063i) q^{80} +(-7.60625 - 7.60625i) q^{81} +(0.277078 - 0.491135i) q^{82} +(-9.93110 + 6.63575i) q^{83} +(8.07245 + 0.367937i) q^{84} +(-6.78626 + 1.34987i) q^{85} +(7.16914 - 0.541586i) q^{86} +(0.631793 - 1.52528i) q^{87} +(-0.563352 + 3.35224i) q^{88} +(3.81437 + 9.20870i) q^{89} +(11.6684 - 5.89927i) q^{90} +(0.409193 + 0.273414i) q^{91} +(-3.68503 + 5.00563i) q^{92} +(3.12134 - 15.6921i) q^{93} +(-2.66496 - 3.40240i) q^{94} -13.3552i q^{95} +(8.97906 + 9.26542i) q^{96} +9.29602i q^{97} +(4.29968 - 3.36777i) q^{98} +(0.516342 - 2.59583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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